Generalized Noseme-Hoover system with four-cluster conservative chaotic flow and circuit implementation of generalized Noseme-Hoover system

Abstract

The invention discloses a generalized Noseme-Hoover system with four-cluster conservative chaotic currents and circuit implementation. The circuit is composed of three main channel circuits and three auxiliary channel circuits. Each main channel circuit is composed of a direct-current voltage source, a battery pack, an operational amplifier, a resistor, a capacitor and an analog ground. The auxiliary channel circuit is composed of a multiplier. Conservative chaos can appear in a Hamiltonian system and can also appear in a constant-temperature system, a typical constant-temperature system such as a Noseme-Hoover system, and physical implementation of the system is similar to that of a dissipation system but does not have ergodicity. When a non-traversal conservative system is applied to an encryption algorithm, regular motion may occur due to improper selection of initial conditions, and the potential risk that encrypted information is cracked exists. If a traversal conservative system is used, this weakness can be overcome. The generalized Noseme-Hoover system provided by the invention can generate four clusters of conservative chaotic flows, has ergodicity, and adds a new thought for the conservative chaotic system in the field of information security.

Description

Technical Field

[0001] The present invention relates to a three-dimensional constant temperature system and its circuit implementation, and particularly to a constant temperature system with four clusters of conservative chaotic flows and its circuit construction. Background Art

[0002] So far, the research on encryption algorithms based on conservative chaos has gradually become one of the hot topics in the application of chaos. Conservative chaos can not only appear in Hamiltonian systems, but also in constant temperature systems. When designing an encryption algorithm using a non-ergodic conservative system, improper selection of the initial conditions may lead to regular motion, increasing the risk of the encrypted information being cracked. While using an ergodic conservative system, the above problems will not occur, thereby improving the stability and reliability of the algorithm. In practical applications, obtaining an accurate Hamiltonian system model is a very challenging task, while a constant temperature system is relatively easy to implement. Therefore, in the field of cryptography, constant temperature systems have broad application prospects. A typical constant temperature system such as the Nosé-Hoover system does not have ergodicity. Currently, only a very small number of low-dimensional conservative constant temperature systems with ergodicity have been proposed. In view of the above situation, the present invention proposes a generalized Nosé-Hoover system and circuit with four clusters of conservative chaotic flows, adding a new idea for conservative chaotic systems in the field of information security. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a generalized Nosé-Hoover system and its circuit implementation with four clusters of conservative chaotic flows. The present invention adopts the following technical means to achieve the object of the invention:

[0004] 1. A generalized Nosé-Hoover system (i) with four clusters of conservative chaotic flows, and its corresponding mathematical model is:

[0005]

[0006] In the formula, x, y, and z are state variables, and the projection of the three-dimensional phase diagram of the system on the X-Y plane is four clusters of conservative chaotic flows.

[0007] 2. The ergodicity of the generalized Nosé-Hoover system (i), which is characterized in that:

[0008] (1) The ergodicity of a chaotic system, also known as space-filling dynamics, can describe that the dynamics will eventually approach all points arbitrarily. The direct method for judging the ergodicity of a system is the Poincaré section. The Poincaré section diagram is an important tool for describing the trajectory motion characteristics in the phase space of a dynamic system. It provides an intuitive measure. If the system is ergodic, it shows no "holes" numerically;

[0009] (2) Obtain the Poincaré section of the system (i) in the X - Y, Y - Z, and X - Z planes with the help of MATLAB.

[0010] 3. A circuit constructed based on the system (i) consists of three main - channel circuits and three auxiliary - channel circuits:

[0011] (1) A circuit constructed based on the system (i) consists of three main - channel circuits and three auxiliary - channel circuits: The first main - channel circuit consists of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U1A, an operational amplifier U1B, and resistors R1, R2, R3, R4, R5, R6, and a capacitor C1; the second main - channel circuit consists of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U2A, an operational amplifier U2B, and resistors R7, R8, R9, R10, R11, R12, R13, and a capacitor C2; the third main - channel circuit consists of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U3A, an operational amplifier U3B, and resistors R14, R15, R16, R17, R18, and a capacitor C3; the first auxiliary - channel circuit consists of multipliers A1, A2, and A3; the second auxiliary - channel circuit consists of multipliers A4, A5, A6, and A7; the third auxiliary - channel circuit consists of multipliers A8, A9, A10, and A11;

[0012] (2) The output of multiplier A2 in the first auxiliary channel circuit is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R1; the output of multiplier A3 in the first auxiliary channel circuit is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R2; the output of multiplier A11 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R3; the output of operational amplifier U1A is connected to the negative input terminal of operational amplifier U1A through capacitor C1; the output terminal of operational amplifier U1A outputs the x signal; the output of operational amplifier U1A is connected to the two input terminals of multiplier A6 in the second auxiliary channel circuit; the output of operational amplifier U1A is connected to the X input terminal of multiplier A7 in the second auxiliary channel circuit; the output of operational amplifier U1A is connected to the negative input terminal of operational amplifier U1B in the first main channel circuit through resistor R5; the positive input terminal of operational amplifier U1A is grounded; the output of operational amplifier U1B is connected to the negative input terminal of operational amplifier U1B through resistor R6; the output terminal of operational amplifier U1B outputs the -x signal; the output of operational amplifier U1B is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R11; the output of operational amplifier U1B is connected to the Y input terminal of multiplier A4 in the second auxiliary channel circuit; the positive input terminal of operational amplifier U1B is grounded; the positive power supply terminal of operational amplifier U1B is connected to DC voltage source VCC; the negative power supply terminal of operational amplifier U1B is connected to DC voltage source VDD;

[0013] (3) The output of multiplier A4 in the second auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R7; the output of multiplier A5 in the second auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R8; the output of multiplier A7 in the second auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R9; the output of multiplier A8 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R10; the output of operational amplifier U2A is connected to the negative input terminal of operational amplifier U2A through capacitor C2; the output terminal of operational amplifier U2A outputs the y signal; the output of operational amplifier U2A is connected to the two input terminals of multiplier A1 in the first auxiliary channel circuit; the output of operational amplifier U2A is connected to the X input terminal of multiplier A9 in the third auxiliary channel circuit; the output of operational amplifier U2A is connected to the Y input terminal of multiplier A11 in the third auxiliary channel circuit; the output of operational amplifier U2A is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R4; the output of operational amplifier U2A is connected to the negative input terminal of operational amplifier U2B in the second main channel circuit through resistor R12; the positive input terminal of operational amplifier U2A is grounded; the output of operational amplifier U2B is connected to the negative input terminal of operational amplifier U2B through resistor R13; the output terminal of operational amplifier U2B outputs the -y signal; the output of operational amplifier U2B is connected to the X input terminal of multiplier A2 in the first auxiliary channel circuit; the output of operational amplifier U2B is connected to the X input terminal of multiplier A8 in the third auxiliary channel circuit; the output of operational amplifier U2B is connected to the Y input terminal of multiplier A9 in the third auxiliary channel circuit; the positive input terminal of operational amplifier U2B is grounded; the positive power supply terminal of operational amplifier U2B is connected to DC voltage source VCC; the negative power supply terminal of operational amplifier U2B is connected to DC voltage source VDD;

[0014] (4) The output of multiplier A9 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U3A in the third main channel circuit through resistor R15; the output of multiplier A10 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U3A in the third main channel circuit through resistor R14; the negative terminal of battery pack V1 is connected to the negative input terminal of operational amplifier U3A in the third main channel circuit through resistor R16; the positive terminal of battery pack V1 is grounded; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3A through capacitor C3; the output terminal of operational amplifier U3A outputs signal z; the output of operational amplifier U3A is connected to the X input terminal of multiplier A3 in the first auxiliary channel circuit; the output of operational amplifier U3A is connected to the X input terminal of multiplier A4 in the second auxiliary channel circuit; the output of operational amplifier U3A is connected to the Y input terminal of multiplier A5 in the second auxiliary channel circuit; the output of operational amplifier U3A is connected to the Y input terminal of multiplier A8 in the third auxiliary channel circuit; the output of operational amplifier U3A is connected to the X input terminal of multiplier A11 in the third auxiliary channel circuit; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3B in the third main channel circuit through resistor R17; the positive input terminal of operational amplifier U3A is grounded; the output of operational amplifier U3B is connected to the negative input terminal of operational amplifier U3B through resistor R18; the output terminal of operational amplifier U3B outputs signal -z; the positive input terminal of operational amplifier U3B is grounded; the positive power supply terminal of operational amplifier U3B is connected to DC voltage source VCC; the negative power supply terminal of operational amplifier U3B is connected to DC voltage source VDD;

[0015] (5) The output of multiplier A1 in the first auxiliary channel circuit is connected to the Y input terminal of multiplier A2 in the first auxiliary channel circuit; the output of multiplier A2 in the first auxiliary channel circuit is connected to the Y input terminal of multiplier A3 in the first auxiliary channel circuit; the output of multiplier A6 in the second auxiliary channel circuit is connected to the Y input terminal of multiplier A7 in the second auxiliary channel circuit; the output of multiplier A7 in the second auxiliary channel circuit is connected to the X input terminal of multiplier A5 in the second auxiliary channel circuit; the output of multiplier A9 in the third auxiliary channel circuit is connected to the two input terminals of multiplier A10 in the third auxiliary channel circuit.

[0016] 4. The models of the operational amplifiers U1A, U1B, U2A, U2B, U3A, and U3B are all LF347N; the models of the multipliers A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, and A11 are all AD633; the DC voltage source VCC is 15V, and the DC voltage source VDD is -15V; the voltage of the battery pack V1 is 1V, and the resistance is 100 kΩ; the capacitance values of the capacitors C1, C2, and C3 are all 10 nF; the resistance values of the resistors R1, R2, R3, R4, R7, R8, R9, R10, R11, R14, R15, and R16 are all 100 kΩ; the resistance values of the resistors R5, R6, R12, R13, R17, and R18 are all 10 kΩ.

[0017] Beneficial effects: The present invention proposes a constant temperature system with four clusters of conservative chaotic flows and gives the circuit implementation of the system. The system has ergodicity, that is, the phenomenon of coexistence of chaos and invariant tori will not occur after arbitrarily selecting the initial value. In the chaos encryption technology, the encrypted information will be very difficult to crack. Description of the Drawings

[0018] Figure 1 It is a schematic diagram of the circuit connection structure of the preferred embodiment of the present invention.

[0019] Figure 2 It is the X-Y plane phase diagram of the present invention

[0020] Figure 3 It is the X-Y plane Poincaré diagram of the present invention.

[0021] Figure 4 It is the Y-Z plane Poincaré diagram of the present invention.

[0022] Figure 5 It is the X-Z plane Poincaré diagram of the present invention. Detailed Embodiments

[0023] The following further describes the present invention in more detail with reference to the drawings and preferred embodiments. See Figures 1 - 5 .

[0024] 1. A generalized Nosé-Hoover system (i) with four clusters of conservative chaotic flows, and the corresponding mathematical model is:

[0025]

[0026] where x, y, and z are state variables, and the projection of the three-dimensional phase diagram of the system on the X-Y plane is four clusters of conservative chaotic flows. See Figure 2 .

[0027] 2. Ergodicity of the generalized Nosé-Hoover system (i), characterized by:

[0028] (1) The ergodicity of a chaotic system, also known as space-filling dynamics, can describe that the dynamics eventually approaches all points arbitrarily closely. The direct method for judging the ergodicity of a system is the Poincaré section. The Poincaré section diagram is an important tool for describing the trajectory motion characteristics in the phase space of a dynamic system. It provides an intuitive measure. If the system is ergodic, numerically it shows no "holes";

[0029] (2) By means of MATLAB, the Poincaré sections of system (i) in the X-Y, Y-Z, and X-Z planes are a chaotic sea, see Figures 3 - 5 .

[0030] 3. See Figure 1 , a circuit constructed based on system (i) consists of three main channel circuits and three auxiliary channel circuits:

[0031] (1) The circuit constructed based on system (i) consists of three main channel circuits and three auxiliary channel circuits: The first main channel circuit consists of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U1A, an operational amplifier U1B, and resistors R1, R2, R3, R4, R5, R6, and a capacitor C1. The second main channel circuit consists of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U2A, an operational amplifier U2B, and resistors R7, R8, R9, R10, R11, R12, R13, and a capacitor C2. The third main channel circuit consists of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U3A, an operational amplifier U3B, and resistors R14, R15, R16, R17, R18, and a capacitor C3. The first auxiliary channel circuit consists of multipliers A1, A2, and A3. The second auxiliary channel circuit consists of multipliers A4, A5, A6, and A7. The third auxiliary channel circuit consists of multipliers A8, A9, A10, and A11;

[0032] (2) The output of multiplier A2 in the first auxiliary channel circuit is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R1; the output of multiplier A3 in the first auxiliary channel circuit is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R2; the output of multiplier A11 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R3; the output of operational amplifier U1A is connected to the negative input terminal of operational amplifier U1A through capacitor C1; the output terminal of operational amplifier U1A outputs the x signal; the output of operational amplifier U1A is connected to the two input terminals of multiplier A6 in the second auxiliary channel circuit; the output of operational amplifier U1A is connected to the X input terminal of multiplier A7 in the second auxiliary channel circuit; the output of operational amplifier U1A is connected to the negative input terminal of operational amplifier U1B in the first main channel circuit through resistor R5; the positive input terminal of operational amplifier U1A is grounded; the output of operational amplifier U1B is connected to the negative input terminal of operational amplifier U1B through resistor R6; the output terminal of operational amplifier U1B outputs the -x signal; the output of operational amplifier U1B is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R11; the output of operational amplifier U1B is connected to the Y input terminal of multiplier A4 in the second auxiliary channel circuit; the positive input terminal of operational amplifier U1B is grounded; the positive power supply terminal of operational amplifier U1B is connected to DC voltage source VCC; the negative power supply terminal of operational amplifier U1B is connected to DC voltage source VDD;

[0033] (3) The output of multiplier A4 in the second auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R7; the output of multiplier A5 in the second auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R8; the output of multiplier A7 in the second auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R9; the output of multiplier A8 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R10; the output of operational amplifier U2A is connected to the negative input terminal of operational amplifier U2A through capacitor C2; the output terminal of operational amplifier U2A outputs the y signal; the output of operational amplifier U2A is connected to the two input terminals of multiplier A1 in the first auxiliary channel circuit; the output of operational amplifier U2A is connected to the X input terminal of multiplier A9 in the third auxiliary channel circuit; the output of operational amplifier U2A is connected to the Y input terminal of multiplier A11 in the third auxiliary channel circuit; the output of operational amplifier U2A is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R4; the output of operational amplifier U2A is connected to the negative input terminal of operational amplifier U2B in the second main channel circuit through resistor R12; the positive input terminal of operational amplifier U2A is grounded; the output of operational amplifier U2B is connected to the negative input terminal of operational amplifier U2B through resistor R13; the output terminal of operational amplifier U2B outputs the -y signal; the output of operational amplifier U2B is connected to the X input terminal of multiplier A2 in the first auxiliary channel circuit; the output of operational amplifier U2B is connected to the X input terminal of multiplier A8 in the third auxiliary channel circuit; the output of operational amplifier U2B is connected to the Y input terminal of multiplier A9 in the third auxiliary channel circuit; the positive input terminal of operational amplifier U2B is grounded; the positive power supply terminal of operational amplifier U2B is connected to DC voltage source VCC; the negative power supply terminal of operational amplifier U2B is connected to DC voltage source VDD;

[0034] (4) The output of multiplier A9 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U3A in the third main channel circuit through resistor R15; the output of multiplier A10 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U3A in the third main channel circuit through resistor R14; the negative terminal of battery pack V1 is connected to the negative input terminal of operational amplifier U3A in the third main channel circuit through resistor R16; the positive terminal of battery pack V1 is grounded; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3A through capacitor C3; the output terminal of operational amplifier U3A outputs signal z; the output of operational amplifier U3A is connected to the X input terminal of multiplier A3 in the first auxiliary channel circuit; the output of operational amplifier U3A is connected to the X input terminal of multiplier A4 in the second auxiliary channel circuit; the output of operational amplifier U3A is connected to the Y input terminal of multiplier A5 in the second auxiliary channel circuit; the output of operational amplifier U3A is connected to the Y input terminal of multiplier A8 in the third auxiliary channel circuit; the output of operational amplifier U3A is connected to the X input terminal of multiplier A11 in the third auxiliary channel circuit; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3B in the third main channel circuit through resistor R17; the positive input terminal of operational amplifier U3A is grounded; the output of operational amplifier U3B is connected to the negative input terminal of operational amplifier U3B through resistor R18; the output terminal of operational amplifier U3B outputs signal -z; the positive input terminal of operational amplifier U3B is grounded; the positive power supply terminal of operational amplifier U3B is connected to DC voltage source VCC; the negative power supply terminal of operational amplifier U3B is connected to DC voltage source VDD;

[0035] (5) The output of multiplier A1 in the first auxiliary channel circuit is connected to the Y input terminal of multiplier A2 in the first auxiliary channel circuit; the output of multiplier A2 in the first auxiliary channel circuit is connected to the Y input terminal of multiplier A3 in the first auxiliary channel circuit; the output of multiplier A6 in the second auxiliary channel circuit is connected to the Y input terminal of multiplier A7 in the second auxiliary channel circuit; the output of multiplier A7 in the second auxiliary channel circuit is connected to the X input terminal of multiplier A5 in the second auxiliary channel circuit; the output of multiplier A9 in the third auxiliary channel circuit is connected to the two input terminals of multiplier A10 in the third auxiliary channel circuit.

[0036] 4. The models of the operational amplifiers U1A, U1B, U2A, U2B, U3A, and U3B are all LF347N; the models of the multipliers A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, and A11 are all AD633; the DC voltage source VCC is 15V, and the DC voltage source VDD is -15V; the voltage of the battery pack V1 is 1V, and the resistance is 100 kΩ; the capacitance values of the capacitors C1, C2, and C3 are all 10 nF; the resistance values of the resistors R1, R2, R3, R4, R7, R8, R9, R10, R11, R14, R15, and R16 are all 100 kΩ; the resistance values of the resistors R5, R6, R12, R13, R17, and R18 are all 10 kΩ.

[0037] Of course, the above description is not a limitation of the invention, and the invention is not limited to the above examples. Changes, modifications, additions, or substitutions made by those of ordinary skill in the art within the scope of the essence of the present invention also fall within the protection scope of the present invention.

Claims

1. A generalized Nosé-Hoover system (i) with four clusters of conservative chaotic flows, and its corresponding mathematical model is: where x, y, and z are state variables, and the projection of the three-dimensional phase diagram of this system on the X-Y plane is four clusters of conservative chaotic flows.

2. The ergodicity of the generalized Nosé-Hoover system (i), which is characterized by: (1) The ergodicity of a chaotic system, also known as space-filling dynamics, can describe that the dynamics will eventually approach all points arbitrarily closely. The direct method for judging the ergodicity of a system is the Poincaré section. The Poincaré section diagram is an important tool for describing the trajectory motion characteristics in the phase space of a dynamic system. It provides an intuitive measure. If the system is ergodic, numerically it shows no "holes"; (2) The Poincaré section of system (i) is a chaotic sea without "holes".

3. A circuit constructed based on system (i) consists of three main-channel circuits and three auxiliary-channel circuits as follows: (1) The circuit constructed based on system (i) consists of three main-channel circuits and three auxiliary-channel circuits: The first main-channel circuit consists of a DC voltage source VCC, a DC voltage source VDD, operational amplifiers U1A and U1B, and resistors R1, R2, R3, R4, R5, R6, and capacitor C1. The second main-channel circuit consists of a DC voltage source VCC, a DC voltage source VDD, operational amplifiers U2A and U2B, and resistors R7, R8, R9, R10, R11, R12, R13, and capacitor C2. The third main-channel circuit consists of a DC voltage source VCC, a DC voltage source VDD, operational amplifiers U3A and U3B, and resistors R14, R15, R16, R17, R18, and capacitor C3. The first auxiliary-channel circuit consists of multipliers A1, A2, and A3. The second auxiliary-channel circuit consists of multipliers A4, A5, A6, and A7. The third auxiliary-channel circuit consists of multipliers A8, A9, A10, and A11; (2) The output of multiplier A2 in the first auxiliary channel circuit is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R1; the output of multiplier A3 in the first auxiliary channel circuit is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R2; the output of multiplier A11 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R3; the output of operational amplifier U1A is connected to the negative input terminal of operational amplifier U1A through capacitor C1; the output terminal of operational amplifier U1A outputs the x signal; the output of operational amplifier U1A is connected to the two input terminals of multiplier A6 in the second auxiliary channel circuit; the output of operational amplifier U1A is connected to the X input terminal of multiplier A7 in the second auxiliary channel circuit; the output of operational amplifier U1A is connected to the negative input terminal of operational amplifier U1B in the first main channel circuit through resistor R5; the positive input terminal of operational amplifier U1A is grounded; the output of operational amplifier U1B is connected to the negative input terminal of operational amplifier U1B through resistor R6; the output terminal of operational amplifier U1B outputs the -x signal; the output of operational amplifier U1B is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R11; the output of operational amplifier U1B is connected to the Y input terminal of multiplier A4 in the second auxiliary channel circuit; the positive input terminal of operational amplifier U1B is grounded; the positive power supply terminal of operational amplifier U1B is connected to DC voltage source VCC; the negative power supply terminal of operational amplifier U1B is connected to DC voltage source VDD; (3) The output of multiplier A4 in the second auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R7; the output of multiplier A5 in the second auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R8; the output of multiplier A7 in the second auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R9; the output of multiplier A8 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U2A in the second main channel circuit through resistor R10; the output of operational amplifier U2A is connected to the negative input terminal of operational amplifier U2A through capacitor C2; the output terminal of operational amplifier U2A outputs the y signal; the output of operational amplifier U2A is connected to the two input terminals of multiplier A1 in the first auxiliary channel circuit; the output of operational amplifier U2A is connected to the X input terminal of multiplier A9 in the third auxiliary channel circuit; the output of operational amplifier U2A is connected to the Y input terminal of multiplier A11 in the third auxiliary channel circuit; the output of operational amplifier U2A is connected to the negative input terminal of operational amplifier U1A in the first main channel circuit through resistor R4; the output of operational amplifier U2A is connected to the negative input terminal of operational amplifier U2B in the second main channel circuit through resistor R12; the positive input terminal of operational amplifier U2A is grounded; the output of operational amplifier U2B is connected to the negative input terminal of operational amplifier U2B through resistor R13; the output terminal of operational amplifier U2B outputs the -y signal; the output of operational amplifier U2B is connected to the X input terminal of multiplier A2 in the first auxiliary channel circuit; the output of operational amplifier U2B is connected to the X input terminal of multiplier A8 in the third auxiliary channel circuit; the output of operational amplifier U2B is connected to the Y input terminal of multiplier A9 in the third auxiliary channel circuit; the positive input terminal of operational amplifier U2B is grounded; the positive power supply terminal of operational amplifier U2B is connected to the DC voltage source VCC; the negative power supply terminal of operational amplifier U2B is connected to the DC voltage source VDD; (4) The output of multiplier A9 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U3A in the third main channel circuit through resistor R15; the output of multiplier A10 in the third auxiliary channel circuit is connected to the negative input terminal of operational amplifier U3A in the third main channel circuit through resistor R14; the negative terminal of battery pack V1 is connected to the negative input terminal of operational amplifier U3A in the third main channel circuit through resistor R16; the positive terminal of battery pack V1 is grounded; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3A through capacitor C3; the output terminal of operational amplifier U3A outputs signal z; the output of operational amplifier U3A is connected to the X input terminal of multiplier A3 in the first auxiliary channel circuit; the output of operational amplifier U3A is connected to the X input terminal of multiplier A4 in the second auxiliary channel circuit; the output of operational amplifier U3A is connected to the Y input terminal of multiplier A5 in the second auxiliary channel circuit; the output of operational amplifier U3A is connected to the Y input terminal of multiplier A8 in the third auxiliary channel circuit; the output of operational amplifier U3A is connected to the X input terminal of multiplier A11 in the third auxiliary channel circuit; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3B in the third main channel circuit through resistor R17; the positive input terminal of operational amplifier U3A is grounded; the output of operational amplifier U3B is connected to the negative input terminal of operational amplifier U3B through resistor R18; the output terminal of operational amplifier U3B outputs signal -z; the positive input terminal of operational amplifier U3B is grounded; the positive power supply terminal of operational amplifier U3B is connected to DC voltage source VCC; the negative power supply terminal of operational amplifier U3B is connected to DC voltage source VDD; (5) The output of multiplier A1 in the first auxiliary channel circuit is connected to the Y input terminal of multiplier A2 in the first auxiliary channel circuit; the output of multiplier A2 in the first auxiliary channel circuit is connected to the Y input terminal of multiplier A3 in the first auxiliary channel circuit; the output of multiplier A6 in the second auxiliary channel circuit is connected to the Y input terminal of multiplier A7 in the second auxiliary channel circuit; the output of multiplier A7 in the second auxiliary channel circuit is connected to the X input terminal of multiplier A5 in the second auxiliary channel circuit; the output of multiplier A9 in the third auxiliary channel circuit is connected to the two input terminals of multiplier A10 in the third auxiliary channel circuit.

4. A generalized Nosé-Hoover system with four clusters of conservative chaotic flows and its circuit implementation according to claim 3, characterized in that: The models of the operational amplifiers U1A, U1B, U2A, U2B, U3A, and U3B are all LF347N; the models of the multipliers A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, and A11 are all AD633; the DC voltage source VCC is 15V, and the DC voltage source VDD is -15V; the voltage of the battery pack V1 is 1V, and the resistance is 100 kΩ; the capacitance values of the capacitors C1, C2, and C3 are all 10 nF; the resistance values of the resistors R1, R2, R3, R4, R7, R8, R9, R10, R11, R14, R15, and R16 are all 100 kΩ; the resistance values of the resistors R5, R6, R12, R13, R17, and R18 are all 10 kΩ.

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