Generator of chaotic oscillations. RU patent 2403672.

FIELD: radio engineering.

SUBSTANCE: generator of chaotic oscillations comprises two resistors, two condensers, induction element, non-linear impedance converter, non-linear current converter and two non-linear voltage converters.

EFFECT: expansion of range for control of generated chaotic signal parametres.

24 dwg

The invention relates to electrical engineering and can be used as a source of chaotic electromagnetic waves.

Known generator of chaotic oscillations (N.Inaba, T.Saito and S.Mori. Chaotic phenomena in a circuit with negative resistance and ideal swith of diodes // The transactions of IEICE, 1987, vol.E 70, No 8, p.744)containing the device with negative resistance, the first output of which is connected with the first findings of the first capacitor and a nonlinear resistor, the second terminal is connected with the second output of the first capacitor and the first findings of the second capacitor and the inductive element, the second, the conclusions of which is connected to the second output of the nonlinear resistor.

Also known generator of chaotic oscillations (Traumata. Chaos in electronic circuits. TIER, 1987, CH, No. 8, p.76-79, 19, 20), containing a capacitor, a first output which is connected to the first output device with negative conductivity, the second terminal of which is connected to the first output of the parallel oscillating circuit, the second terminal of which is connected with the second output capacitor.

The disadvantage of these generators is the limited capability of modifying the chaotic attractor, which limits the possibility of tuning of the parameters of the generated chaotic oscillations.

The closest to the technical nature of the claimed device is generalizations oscillations (Prokopenko VG The generator of chaotic oscillations. Pat. 2273088. Publ. 2006, BIPM No. 9), containing the first and second capacitors, inductive element, a first resistor and a nonlinear impedance Converter.

The disadvantage of this generator of chaotic oscillations is that the properties of the chaotic attractor in it are determined by the characteristics of the only non-linear element, which limits the possibility of tuning of the parameters of the generated chaotic oscillations.

The aim of the invention is an extension of the regulation parameters of the chaotic signal by increasing the possibilities of changing the configuration of the corresponding chaotic attractor.

The purpose of the invention is achieved by the fact that the generator of chaotic oscillations, containing the first and second capacitors, inductive element, a first resistor and a nonlinear impedance Converter, input a second resistor, the first and second non-linear voltage converters and nonlinear Converter current, the first output of which is connected to the first input of the nonlinear output of the impedance Converter and the first output of the first resistor, the second terminal of which is connected with a second input the output of the nonlinear impedance Converter, the first output of which is connected to the first output output of the first nonlinear conversions the user voltage, the second output of which is connected with the second output nonlinear output of the Converter current, the first output output of the second nonlinear voltage Converter and the first output of the second resistor, the second terminal of which is connected with the second output of the output of the second nonlinear voltage Converter and the second output nonlinear output of the impedance Converter, the first and second findings of the first capacitor connected to respective first and second input pins of the first nonlinear voltage Converter, the first and second findings of the second capacitor connected to respective first and second input pins of the second non-linear voltage Converter, the first and second terminals of inductive element connected to respective first and second input pins of the nonlinear Converter current transfer characteristic of the nonlinear transducer impedance is defined by the equation

where i₂(i₁- the current flowing through the weekend conclusions the nonlinear impedance Converter,

i₁the current flowing through the inlet conclusions the nonlinear impedance Converter,

I₀- boundary current between the middle, pohodami is through the origin, segment transfer characteristic of the nonlinear impedance Converter and the adjacent lateral segments of the transfer characteristic of the nonlinear impedance Converter, a and b are real coefficients with opposite signs, M and N are integers, the voltage at the first input the output of the nonlinear transducer impedance is equal to the voltage at the first output of the nonlinear output of the impedance Converter, the voltage at the second input the output of the nonlinear transducer impedance is equal to the voltage at the second output of the nonlinear output of the impedance Converter, transfer characteristics of the first and second non-linear voltage converters and nonlinear transducer defined by the equations U_PN(u_C1)=U₀H₁(w₁), U_PN=u(u_C2)=U₀H₂(w₂and i_FRI(i_L)=I₀H₃(w₃), respectively, where u_PN(u_C1) - AC voltage between the first and second output pins of the first nonlinear voltage Converter, u_C1- AC voltage on the first capacitor, u_PN(u_C2) - AC voltage between the first and second output pins of the second non-linear voltage Converter, uC₂- AC voltage on the second capacitor is, i_FRI(i_L) - AC current flowing through the weekend conclusions

and d_j>>1, M_jand N_j, integers, j=1, 2, 3, alternating current flowing through the output findings of the first non-linear Converter voltage equal to the AC current flowing in the circuit of the first capacitor, an alternating current flowing through the weekend conclusions of the second non-linear Converter voltage equal to the AC current flowing in the circuit of the second capacitor, the voltage between the first and second output pins nonlinear transducer is equal to the voltage between its first and second input pins, each nonlinear voltage Converter includes a voltage amplifier, a noninverting input connected to the first input and the first output conclusions nonlinear voltage Converter, a second input the output of which is connected to the first amplifier output voltage and the first resistor, the second terminal of which is connected to the inverting input of the voltage amplifier and the first output of the nonlinear dvukhpolosnykh, the second terminal of which is connected with the second amplifier output voltage and the second output nonlinear output of the voltage Converter, nonlinear DC Converter includes a voltage amplifier, inv is chirouse an input connected to the second input of the nonlinear transducer and the first output of the nonlinear dvukhpolosnykh, the second output of which is connected to the first amplifier output voltage and the first resistor, the second terminal of which is connected with the second output nonlinear output transducer and reinvestiruet the input of the voltage amplifier, the second output of which is connected with the first input and the first output conclusions nonlinear transducer, nonlinear impedance Converter includes a voltage amplifier, the inverting input of which is connected to the first input of the nonlinear output of the impedance Converter and the first output of the nonlinear dvukhpolosnykh, the second terminal of which is connected to the first amplifier output voltage and the first output line dvukhpolosnykh, the second terminal of which is connected to the first output nonlinear output of the impedance Converter and reinvestiruet the input of the amplifier voltage, the second output of which is connected with the second input and second output conclusions the nonlinear impedance Converter and a common bus, each nonlinear dvukhpolosnykh contains 1+2Max(Q,R), active two-ports, where Max(Q,R) is the greater of the numbers Q and R, which are respectively M and N in nonlinear dvukhpolosnykh, part of the nonlinear impedance Converter, M₁and N₁in nonlinear dvukhpolosnykh that is part of the first non-linear transformations is the user voltage, M₂and N₂in nonlinear dvukhpolosnykh that is part of the second non-linear voltage Converter, M₃and N₃in nonlinear dvukhpolosnykh that is part of a nonlinear transducer, the first and second findings of the first active two-port network are connected respectively with the first and second conclusions nonlinear dvukhpolosnykh and outputs of the respective first and second current generators of nonlinear dvukhpolosnykh common bus which is connected to the first power bus, the third and fourth conclusions each of the previous two-port network are connected respectively with the first and second findings of the subsequent active two-port network, the third and the fourth output, 1+2Max(Q,R)-th active two-port network connected to respective first and second terminals of the resistor, linear dvukhpolosnykh contains a resistor, first and second, the findings of which, which correspond to the first and second conclusions linear dvukhpolosnykh, connected to respective third and fourth pins of the quadrupole, the first and second findings of which are connected to the outputs of the respective first and second current generators linear dvukhpolosnykh common bus which is connected to the first power bus, each active two-port network contains a first and a second transistor which, the emitters of which, which correspond to the first and second pins of the four-terminal network, connected to respective first and second findings of the first resistor, the collector of the first transistor is connected to the emitter of the third transistor and the base of the fourth transistor, the emitter of which is connected to the collector of the fifth transistor and the first output of the second resistor, the second terminal of which is connected to the base of the fifth transistor and the first output of the third resistor, the second terminal of which is connected to the emitter of the fifth transistor, the base of the second transistor and the output of the first current generator, a common bus which is connected to the first power bus and the common bus of the second current generator, the output of which is connected to the base the first transistor, the emitter of the sixth transistor and the first output of the fourth resistor, the second terminal of which is connected to the base of the sixth transistor and the first output of the fifth resistor, the second terminal of which is connected to the collector of the sixth transistor and the emitter of the seventh transistor, the base of which is connected to the collector of the second transistor and the emitter of the eighth transistor, the base and the collector of which is connected to the fourth output of the active two-port network and the output of the third current generator, a common bus which is connected to the collectors of the fourth and seventh transistors, the Torah by the power bus and the common bus, the fourth current generator, the output of which is connected to the base and collector of the third transistor and the third output of the active two-port network, each voltage amplifier includes first and second transistors, bases of which are relevant reinvestiruet and inverting inputs of the voltage amplifier, the emitter of the first transistor of the amplifier is connected to the collector of the third transistor of the amplifier and the base of the fourth transistor of the amplifier, the emitter of which is connected to the output of the first current generator amplifier and the emitter of the third transistor of the amplifier, the base of which is connected to the collector of the fourth transistor of the amplifier and the emitter of the second transistor amplifier, the collector of which is connected to the base of the fifth transistor amplifier and the emitter of the sixth transistor amplifier, the base and the collector of which is connected with the output of the second current generator amplifier and the base of the seventh transistor amplifier, the emitter of which is connected to the collector of the first transistor amplifier, the emitter of the fifth transistor amplifier is connected to the collector of the eighth transistor amplifier and the first output of the first resistor of the amplifier, the second terminal of which is connected to the base of the eighth transistor amplifier and the first output of the second resistor of the amplifier, the second terminal of which is connected to the emitter of the eighth transistor amplifier, the output is the home of the third current generator amplifier and the first amplifier output voltage, the collector of the fifth transistor amplifier connected to the output of the fourth current generator amplifier and emitter of the ninth transistor amplifier, the collector of which is connected to the output of the fifth current generator amplifier and the second amplifier output voltage, the base of the ninth transistor amplifier connected to the third power bus, public bus in the first, third and fifth current generators of the amplifier is connected to the first power bus, the common bus of the second and fourth current generators of the amplifier is connected to the collector of the seventh transistor and the second power bus.

The inventive generator of chaotic oscillations is illustrated by figure 1, which shows its schematic electrical diagram, figure 2, which shows the distribution of currents and voltages in the circuit of the generator during its operation, figure 3, which shows a schematic electrical diagram of the nonlinear voltage Converter, figure 4, which shows a schematic electrical diagram of the nonlinear transducer, figure 5, which shows a schematic electrical diagram of the nonlinear impedance Converter, 6, which shows a schematic electrical diagram of the nonlinear dvukhpolosnykh, Fig.7, which shows the electrical diagram of the active two-port network, Fig, which shows a diagram of the electrical wiring in the practical principle of the amplifier voltage, Fig.9, which shows the dimensionless transfer function of the nonlinear impedance Converter with M=0, N=1, figure 10, which shows the dimensionless transfer function of the nonlinear voltage converters and DC, 11, which shows an example of a projection dimensionless strange attractor on the plane (y,z) for M₁=N₁=M₂=N₂=M₃=N₃=0, M=0, N=1, a=1, b=-0.5, A=10, B=9, C=0.3, Fig illustrating the mechanism of formation of the simplest compound multifactor when M₁=l, N₁=M₂=N₂=M₃=N₃=0, M=0, N=1, a=1, b=-0.5, A=10, B=9, C=0.3, Fig illustrating the mechanism of formation of compound multitracker when M₁=N₁=2, M₂=N₂=M₃=N₃=0, M=0, N=1, a=1, b=-0.5, A=10, B=9, C=0.3, Fig illustrating the mechanism of formation of compound multitracker when M₂=N₂=2, M₁=N₁=M₃=N₃=0, M=0, N=1, a=1, b=-0.5, A=10, B=9, C=0.3, Fig illustrating the mechanism of formation of compound multifactor when M₃=N₃=2, M₁=N₁=M₂=N₂=0, M=0, N=1, a=1, b=-0.5, A=10, B=9, C=0.3, Fig, which includes a three-dimensional image dimensionless strange attractor when M=0, N=1, a=1, b=-0.5, A=10, B=9, C=0.3, M₁=N₁=M₂=N₂=M₃=N₃=1, d₁=d₂=d₃=10, h₁≈0.4, h₂≈5.4, h₃≈2.7, s₁=0, s ≈2.3, s₃≈0.7, Fig, 18 and 19 are examples of the projection of the attractor on the plane (x,y), (x,z) and (y,z), respectively, Fig, 21 and 22, on which the corresponding chaotic attractor on Fig examples of the time-dependent dimensionless x, y and z, Fig, which shows the distribution of currents and voltages in the circuit of the nonlinear voltage Converter during its operation, Fig, which shows the distribution of currents and voltages in the circuit of the nonlinear transducer with his work.

The generator of chaotic oscillations contains the first 1 and second 2 capacitors, inductive element 3, the first 4 and second 5 resistors, non-linear impedance Converter 6, the first 7 and second 8 nonlinear voltage converters, nonlinear current transducer 9, each of the nonlinear voltage Converter includes a voltage amplifier 10, a resistor 11 and nonlinear dvukhpolosnykh 12, nonlinear DC Converter includes a voltage amplifier 13, a resistor 14 and nonlinear dvukhpolosnykh 15, nonlinear impedance Converter includes a voltage amplifier 16, a linear dvukhpolosnykh 17 and nonlinear dvukhpolosnykh 18, line dvukhpolosnykh contains a resistor 19, the active two-port network 20, the first 21 and second 22 generators linear dvukhpolosnykh, nonlinear dvukhpolosnykh contains the resistor 23, the active h is trehpolyusny 24, the first 25 and second 26 generators nonlinear dvukhpolosnykh, each active two-port network includes the first 27 and second 28, 29 third, fourth, 30, 31 fifth, sixth, 32, 33 seventh and eighth transistors 34, the first 35 and second 36, third, 37, 38 fourth and fifth resistors 39, the first 40, 41 second, third 42 and fourth 43 current generators, each voltage amplifier includes the first 44 and second 45, the third 46, 47 fourth, fifth, 48, 49 sixth, seventh, 50, 51 eighth and ninth transistors 52 amplifier, the first 53 and second 54 resistors of the amplifier, the first 55, 56 second, third 57 58 fourth and fifth 59 the current generators of the amplifier.

We write the equations describing the operation of this generator (see figure 2):

where C1 and C2 is a capacitance of the first 1 and second 2 capacitors; L is the inductance of the inductive element 3; R1 and R2 are the resistance, respectively, of the first 4 and second 5 resistors; u_C2and u_C2variable voltage on the first 1 and second 2 capacitors, respectively; i_C1and i_C2, variable currents flowing in the circuits of the first 1 and second 2 capacitors, respectively; u_Land i_L- AC voltage on the inductive element 3 and flowing through him alternating current, respectively.

Considering that

and solving the equation (1) on derivatives

we get the following system of differential equations:

where

Introducing dimensionless variablesand the dimensionless timeimagine the equations in dimensionless form:

where

- dimensionless transfer function of the nonlinear impedance Converter.

From figure 10, which shows the function H/Wj), we see that it is a piecewise-linear multi function containing M_j+N_j+1 segments with unit slope and M_j+N_jsegments with slope-d_j. The length of the argument (x, y, or z) of the segments with unit slope equal to 2h_jthe length of the argument segments with slope-d_jequal to 2h_j/d_j. The coefficient s_jspecifies the offset of the function H_j(w_j), relative to the origin along passing through the origin of the segment with unit slope is m

This nonlinearity of the transmission characteristics of the first and second voltage converters and Converter current is needed in order to provide conditions for the formation of compound multitracker.

When M₁=N₁=M₂=N₂=M₃=N₃=0 when H₁(x)=x, H₂(y)=y, H₃(z)=z, declared the generator of chaotic oscillations generate chaotic oscillations, corresponding to the equations:

For example, when M=0, N=1, a=1, b=-0.5, A=10, B=9, C=0.3, M₁=N₁=M₂=N₂=M₃=N₃=0, the senior characteristic Lyapunov exponent approximately equal to 0.77 (11)

We now put M₁=1, leaving N₁=M₂=N₂=M₃=N₃=0. The function H₁(x) takes the form shown in Fig In this case, the appearance of oscillations in the oscillator will depend on the values of the coefficients of h₁and s₁specifying the position of the boundary between segments nonlinear function H₁(x).

While these boundaries do not intersect with the attractor, fluctuations in the generator will not be different from the case of a linear function H₁(x)=x, so as movement along the x coordinate is on the segment of the function H₁(x) with unit slope passing through the origin. However, the decrease in h₁to 0.4 when the maximum size of the attractor according to the ordinate axis x will exceed the corresponding dimensions of this segment, the phase trajectory will sometimes cross the border between the segments and move on to the segment with slope-d and then to the neighboring segment with unit slope.

When the operating point within the second linear segment with a unit slope fluctuations occur in the generator in accordance with the equations:

because the second linear segment with a unit slope offset from the first axis x on the interval [2h-s]. If we make the change of variables x1=x-2h+s and note thatwe get the system of equations

which is no different from equation (1). Therefore, when the movement on the second segment with a unit slope reproduces the original chaotic attractor, offset from the original on the interval [2h-s] axis X.

When the path again crosses the boundary between segments, the movement will return to the original chaotic attractor, etc. the result is a compound chaotic attractor, uniting two of the same attractor (Fig). Similarly formed integral multitracker with a larger number of Semenov in the composition function H₁(x) (Fig).

Similarly, the formation of compound multifraction, consisting of copies of the original attractor, ordered golosa y and z, - for this are the non-linearity of the second non-linear voltage Converter and nonlinear transducer (Fig and pig, respectively).

If both are nonlinear two functions H_j(w_j), in the manner described are implemented "two-dimensional" composite multitracker (Fig, 18 and 19).

And finally, when all three functions H_j(w_jcontain multiple segments with unit slope, and forms a three-dimensional compound multitracker, an example of which is shown in Fig the description.

The older values of characteristic Lyapunov exponent for different values of the coefficients of equations (3)corresponding to the above situations is equal to:

When M=0, N=1, a=1, b=-0.5, A=10, B=9, C=0.3

in the case of M₁=N₁=M₂=N₂=M₃=N₃=0, the senior characteristic Lyapunov exponent approximately equal to 0.17 (Fig);

in the case of M₁=N₁=1, M₂=N₂=M₃=N₃=0, d₁=10, h₁≈0.4, s₁=0 senior characteristic Lyapunov exponent approximately equal to 0.17 (Fig);

in the case of M₂=N₂=1, M₁=N₁=M₃=N₃=0, d₂=10, h₂≈5.4, s₂≈-2.3 senior characteristic Lyapunov exponent approximately equal to 0.18 (Fig);

in the case of M₃=N₃=1, M₁=N₁=M₂=N₂ =0, d₃=10, h₃≈2.7, s₃≈0.7 senior characteristic Lyapunov exponent approximately equal to 0.18 (Fig);

in the case of M₁=N₁=M₂=N₂=M₃=N₃=1, d₁=d₂=d₃=10, h₁≈0.4, h₂≈5.4, h₃≈2.7, s₁=0, s₂≈-2.3, s₃≈-0.7 senior characteristic Lyapunov exponent is close to 0.18 (Fig).

When these values of the coefficients a, b, a, b, C, M, N, M_jN_jd_jh_j, s_j, j=1, 2, 3 in the proposed generator are observed chaotic oscillations, characterized by the presence of a compound of strange multitracker consisting of multiple copies of the chaotic attractor is shown in figure 11.

The parameters of the transfer characteristic of the nonlinear transducer impedance equal to

where R3 is the resistance of resistor 19, a part of the linear dvukhpolosnykh 17; R4 is the resistance of the first resistor 35, contained in the active two-port network 20 that is part of the linear dvukhpolosnykh 17; R5 is the resistance of the first resistor 35, contained in the first active two-port network 24 that is part of the nonlinear dvukhpolosnykh 18 contained in nonlinear impedance Converter; R6 - a is included in the nonlinear dvukhpolosnykh the resistance of the resistor 23 and the resistance of the first resistors 35, contained in the other, with the second 1+2Max(M,N)-th, active two-ports 24 that are included with nonlinear dvukhpolosnykh 18 contained in nonlinear impedance Converter.

When M=N the current I₁equal to the value of the output currents of the third 42 and fourth 43 generators included in the active two-port 24 contained in nonlinear dvukhpolosnykh 18 that is part of the nonlinear impedance Converter. The value of the output currents I₂generators 25 and 26 contained in nonlinear dvukhpolosnykh 18 that is part of the nonlinear impedance Converter are determined by the expression I₂=KI₁where K=1+2Max(M,N) is the number of active two-ports 24 in the structure of nonlinear dvukhpolosnykh 18, part of the nonlinear impedance Converter. The value of the output currents I₃the third 42 and fourth 43 generators included in the active two-port network 20 that is contained in the linear dvukhpolosnykh 17, is equal to the value of the output currents I₄it contains current generators 21 and 22, I₃=I₄. Moreover, the values of the currents I₃and I₄defined by the expressionwhere |a| and |b| is the absolute value of the coefficients a and b.

The case of M>N is different from case M=N so that the output currents of the third current generators 42 included in SOS is AB 2(M-N)-th and 2(M-N)-1 active two-ports 24, contained in nonlinear dvukhpolosnykh 18 that is part of the nonlinear impedance Converter, respectively incremented and decremented by the same amount ΔI=(0.7...0.9)I₁.

Case N>M differs from M=N so that the output current of the fourth current generators 43, part 2(N-M)-th and 2(N-M)-1 active two-ports 24 contained in nonlinear dvukhpolosnykh 18 that is part of the nonlinear impedance Converter, respectively incremented and decremented by the same amount ΔI=(0.7...0.9)I₁.

The parameters of the transfer characteristic of the j-th nonlinear voltage Converter is equal toprovided thatwhere R7_jthe resistor 11, a part of the j-th nonlinear voltage Converter; R8_j- resistance of the first resistor 35, contained in the first active two-port network 24 that is part of the nonlinear dvukhpolosnykh 12 contained in the j-th nonlinear voltage Converter; R9_j- the value of the resistance part of the nonlinear dvukhpolosnykh 12 of the resistor 23 and the resistance of the first resistors 35, contained in the other, with the second 1+mAh{M_jN_{j )-th, active two-ports 24 that are included with nonlinear dvukhpolosnykh 12 contained in the j-th nonlinear voltage Converter.}

_{When Mj=Njcurrent I1jand J1jequal to the values of the output currents, respectively, third 42 and fourth 43 current generators that are included with odd, except for the first, active two-ports 24, and the values of the output currents, respectively, 43 fourth and third 42 of the generators included in the even-numbered active two-ports 24 contained in nonlinear dvukhpolosnykh 12 that is part of the j-th nonlinear voltage Converter. The value of the output currents I2j, generators 25 and 26 contained in nonlinear dvukhpolosnykh 12 that is part of the j-th nonlinear voltage Converter are determined by the expression I2j=Kj(I1j+J1j)+I3jwhere Kj=Max(MjNj), I3j- the value of the output currents of the third 42 and fourth 43 generators included in the first active quadrupole 24 contained in nonlinear dvukhpolosnykh 12 that is part of the j-th nonlinear voltage Converter, and the current I3jseveral times greater than current Max(I1jI ,J1j), where Max(I1jI ,J1j- the maximal current (I1jJ1ji.e. I3j=(2...5)Max(I1jI ,J1j ).}

_{The case Mj<Njdifferent from the case of Mj=Njthe fact that the output current of the third 42 current generator, part 1+2(Nj-Mj)-th active quadrupole 24 contained in nonlinear dvukhpolosnykh 12 that is part of the j-th nonlinear voltage Converter, is set equal to the current I3j,and the output current of the third 42 current generator included in the first active quadrupole 24 contained in nonlinear dvukhpolosnykh 12 that is part of the j-th nonlinear voltage Converter, is set equal to the current I1j.}

The case of N_j<M_jdifferent from the case of M_j=N_jthe fact that the output current of the fourth 43 current generator, part 1+2(M_j-N_j)-th active quadrupole 24 contained in nonlinear dvukhpolosnykh 12 that is part of the j-th nonlinear voltage Converter equal to the current I_3jand the output current of the fourth 43 current generator included in the first active quadrupole 24 contained in nonlinear dvukhpolosnykh 12 that is part of the j-th nonlinear voltage Converter, is set equal to a current of J_1j.

The parameters of the transfer characteristic of the nonlinear transducer is equal to despite the fact thatwhere R10 is the resistance of resistor 14, part of the nonlinear transducer;

R11 is the resistance of the first resistor 35, contained in the first active two-port network 24 that is part of the nonlinear dvukhpolosnykh 15 contained in nonlinear Converter current; R12 is - is included in the nonlinear dvukhpolosnykh 15 of the resistor 23 and the resistance of the first resistors 35, contained in the other, with the second 1+2Max(M₃N₃)-th, active two-ports included in the nonlinear dvukhpolosnykh 15 contained in nonlinear inverter current.

When M₃=N₃current I₁₃and J₁₃equal to the values of the output currents, respectively, 43 fourth and third 42 current generators that are included with odd, except for the first, active two-ports 24, and the values of the output currents, respectively, third 42 and fourth 43 generators included in the even-numbered active two-ports 24 contained in nonlinear dvukhpolosnykh 15, part of a non-linear transducer. The value of the output currents I₂₃generators 25 and 26 contained in nonlinear dvukhpolosnykh 15, part of a nonlinear Converter that is a, determined by the expression I₂₃=K₃(I₁₃+J₁₃)+I₃₃where K₃=Max(M₃N₃), I₃₃- the value of the output currents of the third 42 and fourth 43 generators included in the first active quadrupole 24 contained in nonlinear dvukhpolosnykh 15, part of a non-linear current transformer, and the current I₃₃several times greater than the current Max(I₁₃I ,J₁₃), where Max(I₁₃I ,J₁₃- the maximal current (I₁₃and J₁₃i.e. I₃₃=(2...5)Max(I₁₃I ,J₁₃).

The case M₃<N₃different from the case of M₃=N₃the fact that the output current of the third 42 current generator, part 1+2(N₃-M₃)-th active quadrupole 24 contained in nonlinear dvukhpolosnykh 15, part of a non-linear transducer, is set equal to the current I₃₃and the output current of the third 42 current generator, a part of Pirogovo active quadrupole 24 contained in nonlinear dvukhpolosnykh 15, part of a non-linear transducer, is set equal to a current of J₁₃.

The case of N₃<M₃different from the case of M₃=N₃the fact that the output current of the fourth 43 current generator, part 1+2(M₃-N₃)-th active quadrupole 24 contained in the non-linear DV is polynice 15, part of the nonlinear Converter of a current equal to the current I₃₃and the output current of the fourth 43 current generator included in the first active quadrupole 24 contained in nonlinear dvukhpolosnykh 15, part of a non-linear transducer, is set equal to the current I₁₃.

The resistance of the second 36, third, 37, 38 fourth and fifth resistors 39 and output currents of the first 40 and second 41 current generators contained in each of the active two-port network, connected by the following relations I₅R14=(1.2...2)U_EB, R13=(1...10)R14 where R13 is the value of resistance of the second 36 and 39 fifth resistors R14 - value resistors 37 third and fourth resistors 38, I₅- the value of the output currents of the first 40 and second 41 generators, U_EB- is basic-emitter narazenia 31 fifth and sixth transistors 32, forming part of the active two-port network.

Output currents of the current generators contained in the voltage amplifier must meet the following ratios I_y1=2I_y2, I_y3+I_y5=I_y4where I_y1- output current of the first 55 current generator amplifier, I_y2- the current output of the second generator 56 current amplifier, I_y3- output current of the third 57 current generator amplifier, I_y4- output current fourth 58 current generator strengthen the La, I_y5- output current fifth 59 current generator amplifier.

Moreover, the values of the currents I_y3and I_y5must be several times greater than the value of the output currents of the first 25 and second 26 current generators contained in nonlinear dvukhpolosnykh, part of the nonlinear impedance Converter, the first or second non-linear converters current or non-current transformer with the voltage amplifier.

The resistance of the first 53 and second 54 resistors of the amplifier and the output current of the third 57 current generator contained in the voltage amplifier, connected by the following relations I_y3R15=(1.2...2)U_EB, R15=(1...10)R16, where R15 and R16 is, the resistance values of the first 53 and second 54 resistors of the amplifier, U_EB- is basic-emitter narazenia 51 eighth transistor amplifier.

The first and second voltage converters are nonlinear impedance converters, which work as follows (Fig).

The voltage Converter includes a differential voltage amplifier with high gain, with additional current output. The amplifier has a high input impedance at both inputs and low output impedance at the first output. Additional (second) output represents the output of the repeater power supply with you okim output resistance. Its purpose is to generate a current equal to a current flowing through the first low impedance output of the amplifier, so that an alternating current flowing in the first output of the amplifier was equal to the alternating current flowing from the second output of the amplifier (Fig).

Considering the fact that the potential difference between the inputs of the voltage amplifier and the input currents are negligibly small, the voltage drop across the resistor R1 is equal to the voltage drop u_Con the capacitor, therefore, the current i₁flowing in the resistor is equal to u_c/R1, the same current flows in the circuit of the nonlinear resistor R_NLthe voltage which depends on the magnitude of the flowing current through it i₁and consequently, the voltage across the capacitor u_MO(i₁)=u_MO(u_C/R₁).

Due to the negligible potential difference between the inputs of the amplifier, the voltage between the first and second outputs of the nonlinear Converter voltage equal to the drop of the voltage nonlinear resistor u_MO(u_C/R1). Thus the current flowing through the capacitor is equal to the sum of the current i₁flowing in the circuit of the resistors R1 and R_NLand current i_C-i₁flowing in the circuit of the first and second outputs of the amplifier. Therefore, through the output of a nonlinear inverter current flows equal to the current flowing through condens the tor (Fig). That is implemented is specified in the formula of the dependence of u_MO(u_C).

Nonlinear current transducer is a non-linear impedance Converter, which works as follows (Fig). It contains the same amplifier, and a non-linear voltage converters. Since the potential difference between the inputs of the amplifier is negligible, the voltage between the outputs of the nonlinear transducer is equal to the voltage across the inductive element, in addition to equal the voltage on the linear and nonlinear resistors. Through the nonlinear resistor current flow equal to the current in the inductive circuit element. As a result, the nonlinear resistor occurs depending on the magnitude of the current in the inductive element, the voltage drop u_FRI(i_L), under which the chain linear resistor flows a current i_FRI(i_L)=u_FRI(i_L)/R1. At first, low impedance, the output of the amplifier receives the current i_L-i_FRI(i_L), the same current flows from the second amplifier output and the sum current i_Lflows in the external circuit. That is, the external circuit receives a current flowing in the circuit of line resistor i_FRI(i_L).

Thus, when connecting inductive element to an external circuit through a non-linear Converter current through the outputs of the inverter current flows _FRI(i_L), and between them decreases the voltage u_L. That is implemented is specified in the formula of the dependence of i_FRI(i_L).

An example of practical implementation of the selected generator of chaotic oscillations can serve as a scheme with the following parameters.

Let R1=1 kω, C1=0.1 µf, R3=4 kω, R5=500 Ohms, R7₁=R7₂=R10=11 kω, I₀=333 µa. Then if M₁=N₁=M₂=N₂=M₃=N₃=1, d₁=d₂=d₃=10, h₁≈0.4 h₂≈5.4, h₃≈2.7, s₁=0, s₂≈-2.3, s₃≈0.7, M=0, N=1, a=1, b=-0.5, A=10, B=9, C=0.3, chaotic oscillations corresponding to these parameters of equations (3), are observed at the following values of the oscillating system generator:₂≈0.01 µf, L1≈11 mH, R2≈3.3 kω, the nonlinear impedance Converter: R4≈800 Ohms, R6≈333 Ω, I₁≈1 mA; I₂≈3 mA and I₃=I₄≈3 mA, the first nonlinear voltage Converter: R8₁≈11 kω, R9₁≈1 K, I₁₁=J₁₁≈145 μa, I₂₁≈0.79 mA, I₃₁≈0.5 mA, the second non-linear voltage Converter: R8₂≈11 kω, R9₂≈1 K, I₁₂≈1 mA, J₁₂≈ 3 mA and I₂₂≈12 mA; I₃₂≈8 mA, nonlinear transducer: R11≈11 kω, R12≈1 K, I₁₃≈0.75 mA, J₁₃≈1.25 mA; I₂₃≈6 mA; I₃₃≈4 mA, voltage amplifier:

R15≈10 kω, R16≈1 K, I_y1≈400 µa, I_y2≈200 µa, I_y =I_y5≈7.5 mA, I_y4≈15 mA, the bias circuits for constant voltage in the non-linear converters of voltage and current: R13≈5 kω, R14≈1 K, I₅≈1 mA.

Corresponding to these values of the parameters of the generator examples dimensionless strange attractor, its projection on the plane (x,y), (x,z) and (y,z), as well as examples of the dependences of the dimensionless variables x, y and z from the time shown on Fig-22.

Thus, the claimed generator of chaotic oscillations differs from prototype and analogues in which the chaotic signal reconstruction is possible only by changing the parameters of the original chaotic attractor, because it enables you to implement a compound chaotic multifractal received by the amalgamation of the original chaotic attractor with one or more copies thereof, as a result of its restructuring, you can also change the number and mutual arrangement of its constituent components, making the claimed generator has a bigger potential for tuning of the parameters of the generated chaotic signal.

The generator of chaotic oscillations, containing the first and second capacitors, inductive element, a first resistor and a nonlinear impedance Converter, characterized in that it introduced a second resistor, the first is the first and the second non-linear voltage converters and nonlinear current transducer the first output of which is connected to the first input of the nonlinear output of the impedance Converter and the first output of the first resistor, the second terminal of which is connected with a second input the output of the nonlinear impedance Converter, the first output of which is connected to the first output output of the first nonlinear voltage Converter, the second output of which is connected with the second output nonlinear output of the Converter current, the first output output of the second nonlinear voltage Converter and the first output of the second resistor, the second terminal of which is connected with the second output of the output of the second nonlinear voltage Converter and the second output nonlinear output of the impedance Converter, the first and second findings of the first capacitor connected to respective first and the second input pins of the first nonlinear voltage Converter, the first and second findings of the second capacitor connected to respective first and second input pins of the second non-linear voltage Converter, the first and second terminals of inductive element connected to respective first and second input pins of the nonlinear transducer, the transfer characteristic of the nonlinear transducer impedance is defined by the equation

where i₂(i₁- the current flowing through the weekend conclusions the nonlinear impedance Converter, i₁the current flowing through the inlet conclusions the nonlinear impedance Converter,

I₀- boundary current between the medium passing through the origin, the segment of the transfer characteristic of the nonlinear impedance Converter and the adjacent lateral segments of the transfer characteristic of the nonlinear impedance Converter, a and b are real coefficients with opposite signs, M and N are integers, the voltage at the first input the output of the nonlinear transducer impedance is equal to the voltage at the first output of the nonlinear output of the impedance Converter, the voltage at the second input the output of the nonlinear transducer impedance is equal to the voltage at the second output of the nonlinear output of the impedance Converter, transfer characteristics of the first and second non-linear voltage converters and nonlinear transducer defined by the equations u_PN(u_C1)=U₀H₁(w₁), u_PN=(u_C2)=U₀H₂(w₂and i_FRI(i_L)=I₀H₃(w₃), respectively, where u_PN(u_C1) - changes the Noah voltage between the first and second output pins of the first nonlinear voltage Converter, u_C1- AC voltage on the first capacitor, u_PN(u_C2) - AC voltage between the first and second output pins of the second non-linear voltage Converter, u_C2- AC voltage on the second capacitor, i_FRI(i_L) - AC current flowing through the weekend conclusions nonlinear Converter current, i_L- AC current flowing in the inductive circuit element,,,,, R1 is the resistance of the first resistor,

,
,
,
,d_jh_jand s_jmaterial coefficients, and d_j>>1, M_jand N_j- non-negative integers, j=1, 2, 3, alternating current flowing through the output findings of the first non-linear Converter voltage equal to the AC current flowing in the circuit of the first capacitor, an alternating current flowing through the weekend conclusions of the second non-linear Converter voltage equal to the AC current flowing in the circuit of the second capacitor, the voltage between the first and second output pins of the nonlinear Converter current is equal to the voltage between its first and second input pins, each nonlinear voltage Converter includes a voltage amplifier, a noninverting input connected to the first input and the first output conclusions nonlinear voltage Converter, a second input the output of which is connected to the first amplifier output voltage and the first resistor, the second terminal of which is connected to the inverting input of the voltage amplifier and the first output of the nonlinear dvukhpolosnykh, the second terminal of which is connected with the second amplifier output voltage and the second output nonlinear output of the voltage Converter, nonlinear DC Converter includes a voltage amplifier, the inverting input of which is connected to a second input of the nonlinear transducer and the first output of the nonlinear dvukhpolosnykh, the second terminal of which is connected to the first output the voltage amplifier and the first resistor, the second terminal of which is connected with the second output nonlinear output transducer and reinvestiruet the input of the voltage amplifier, the second output of which is connected with the first input and the first output conclusions nonlinear transducer, nonlinear impedance Converter includes a voltage amplifier, the inverting input of which is connected to the first input of the nonlinear output of the impedance Converter and the first output of the m nonlinear dvukhpolosnykh, the second output of which is connected to the first amplifier output voltage and the first output line dvukhpolosnykh, the second terminal of which is connected to the first output nonlinear output of the impedance Converter and reinvestiruet the input of the voltage amplifier, the second output of which is connected with the second input and second output conclusions the nonlinear impedance Converter and a common bus, each nonlinear dvukhpolosnykh contains 1+2Max(Q,R), active two-ports, where Max(Q, R) is the greater of the numbers Q and R, which are respectively M and N in nonlinear dvukhpolosnykh, part of the nonlinear impedance Converter, M₁and N₁in nonlinear dvukhpolosnykh that is part of the first nonlinear voltage Converter, M₂and N₂in nonlinear dvukhpolosnykh that is part of the second non-linear voltage Converter, M₃and N₃in nonlinear dvukhpolosnykh that is part of a nonlinear transducer, the first and second findings of the first active two-port network are connected respectively with the first and second conclusions nonlinear dvukhpolosnykh and outputs of the respective first and second current generators of nonlinear dvukhpolosnykh common bus which is connected to the first power bus, the third and fourth conclusions of each predyduschego quadrupole connected respectively with the first and second findings of the subsequent active two-port network, the third and fourth output, 1+2Max(Q, R)th, the active two-port network connected to respective first and second terminals of the resistor, linear dvukhpolosnykh contains a resistor, the first and second findings of which, which correspond to the first and second conclusions linear dvukhpolosnykh, connected to respective third and fourth pins of the quadrupole, the first and second findings of which are connected to the outputs of the respective first and second current generators linear dvukhpolosnykh common bus which is connected to the first power bus, each active two-port network includes first and second transistors, the emitters of which, which correspond to the first and the second pins of the four-terminal network, connected to respective first and second findings of the first resistor, the collector of the first transistor is connected to the emitter of the third transistor and the base of the fourth transistor, the emitter of which is connected to the collector of the fifth transistor and the first output of the second resistor, the second terminal of which is connected to the base of the fifth transistor and the first output of the third resistor, the second terminal of which is connected to the emitter of the fifth transistor, the base of the second transistor and the output of the first current generator, a common bus which is connected to the first power bus and the shared bus is done of the current generator, the output of which is connected to the base of the first transistor, the emitter of the sixth transistor and the first output of the fourth resistor, the second terminal of which is connected to the base of the sixth transistor and the first output of the fifth resistor, the second terminal of which is connected to the collector of the sixth transistor and the emitter of the seventh transistor, the base of which is connected to the collector of the second transistor and the emitter of the eighth transistor, the base and the collector of which is connected to the fourth output of the active two-port network and the output of the third current generator, a common bus which is connected to the collectors of the fourth and seventh transistors, the second power bus and the common bus, the fourth current generator, the output of which is connected to the base and collector the third transistor and the third output of the active two-port network, each voltage amplifier includes first and second transistors, bases of which are relevant reinvestiruet and inverting inputs of the voltage amplifier, the emitter of the first transistor of the amplifier is connected to the collector of the third transistor of the amplifier and the base of the fourth transistor of the amplifier, the emitter of which is connected to the output of the first current generator amplifier and the emitter of the third transistor of the amplifier, the base of which is connected to the collector of the fourth transistor of the amplifier and Amy is the PC of the second transistor amplifier, the collector of which is connected to the base of the fifth transistor amplifier and the emitter of the sixth transistor amplifier, the base and the collector of which is connected to the output of the second current generator amplifier and the base of the seventh transistor amplifier, the emitter of which is connected to the collector of the first transistor amplifier, the emitter of the fifth transistor amplifier is connected to the collector of the eighth transistor amplifier and the first output of the first resistor of the amplifier, the second terminal of which is connected to the base of the eighth transistor amplifier and the first output of the second resistor of the amplifier, the second terminal of which is connected to the emitter of the eighth transistor amplifier, the output of the third current generator amplifier and the first amplifier output voltage, the collector of the fifth transistor amplifier connected to the output of the fourth current generator amplifier and emitter of the ninth transistor amplifier, the collector of which is connected to the output of the fifth current generator amplifier and the second amplifier output voltage, the base of the ninth transistor amplifier connected to the third power bus, public bus in the first, third and fifth current generators of the amplifier is connected to the first power bus, the common bus of the second and fourth current generators of the amplifier is connected to the collector of the seventh transistor and the second power bus.