Three-dimensional conservative chaotic system with dissipative item and without external force item

Abstract

The invention discloses a three-dimensional conservative chaotic system containing a dissipation item and without an external force item, a circuit of the system is composed of three channel circuits, and each of the three channel circuits is composed of a direct-current voltage source, an operational amplifier, a multiplier, a resistor, a capacitor and an analog ground. At present, continuous systems capable of generating conservative chaos are roughly divided into two types: a high-dimensional system (four-dimensional and above) only containing a conservative term and a three-dimensional system containing the conservative term and an external force term. That is to say, a three-dimensional conservative chaotic system containing a dissipation item but not an external force item does not appear so far. Aiming at the current situation, the invention provides a three-dimensional system capable of generating conservative chaos on the basis of the Shilnikov theorem, and the system contains a dissipation item and does not contain an external force item. In addition, the invention also provides circuit simulation of the system, which is of great significance for verifying physical implementation of conservative chaos.

Description

Technical Field

[0001] The invention relates to the field of chaos, and in particular to a three-dimensional conservative chaotic system containing dissipative terms but without external force terms. Background Art

[0002] Since Sprott proposed the Sprott A system in 1994, conservative chaos has gradually entered the forefront of nonlinear scientific research. Since the dissipative chaos attractor can be reconstructed through the time-delay embedding method, the encryption algorithm based on dissipative chaos may have potential cracking risks. In contrast, conservative chaos can resist such risks to a certain extent due to the lack of attractor structure. In addition, conservative chaos also shows higher complexity than dissipative chaos due to its strong ergodic characteristics, which further highlights the importance of building a conservative chaos system.

[0003] So far, continuous systems that can produce conservative chaos can be roughly divided into two categories: high-dimensional systems (four dimensions and above) containing only conservative terms and three-dimensional systems containing conservative terms and external force terms. It is worth noting that there is no three-dimensional conservative chaotic system with dissipative terms but no external force terms. Given the unique advantages of conservative chaos in the field of information encryption, exploring conservative chaotic systems with diverse structures will not only help deepen and expand chaos theory, but also have a far-reaching impact on improving the security of encryption technology. Summary of the invention

[0004] The purpose of the present invention is to provide a three-dimensional conservative chaotic system with dissipative terms but without external force terms.

[0005] In order to achieve the above object, the solution of the present invention is:

[0006] 1. A three-dimensional conservative chaotic system with dissipative terms but no external force terms, characterized in that:

[0007] (1) A three-dimensional conservative chaotic system (i) with dissipative terms but no external force terms is:

[0008]

[0009] Where x, y, z are state variables;

[0010] (2) A circuit constructed based on system (i), the system comprising three channel circuits: the first channel circuit comprises a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U1A, an operational amplifier U2A, a resistor R1, a resistor R2, a resistor R3, a resistor R4, a resistor R5, a multiplier A1, a multiplier A2, a capacitor C1 and an analog ground; the second channel circuit comprises a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U3A, an operational amplifier U4A, a resistor R6, a resistor R7, a resistor R8, a resistor R9, a resistor R10, a multiplier A8, a multiplier A3, a capacitor C2 and an analog ground; the third channel circuit comprises a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U5A, an operational amplifier U6A, a resistor R11, a resistor R12, a resistor R13, a resistor R14, a resistor R15, a multiplier A4, a multiplier A5, a multiplier A6, a multiplier A7, a capacitor C3 and an analog ground;

[0011] (3) The output of the multiplier A1 in the first channel circuit is connected to the X input terminal of the multiplier A2; the output of the multiplier A2 is connected to the negative input terminal of the operational amplifier U2A through the resistor R2; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U2A through the capacitor C1; the output terminal of the operational amplifier U2A outputs the x signal; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U1A through the resistor R4; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U2A in the first channel circuit through the resistor R1; the output of the operational amplifier U2A is connected to the two input terminals of the multiplier A4 in the third channel circuit; the positive input terminal of the operational amplifier U2A The terminal is grounded; the positive power supply terminal of the operational amplifier U2A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U2A is connected to the DC voltage source VDD; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U1A through the resistor R5; the output terminal of the operational amplifier U1A outputs a -x signal; the output of the operational amplifier U1A is connected to the Y input terminal of the multiplier A2 in the first channel circuit; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U3A in the second channel circuit through the resistor R8; the positive input terminal of the operational amplifier U1A is grounded; the positive power supply terminal of the operational amplifier U1A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U1A is connected to the DC voltage source VDD;

[0012] (4) The output of multiplier A8 in the second channel circuit is connected to the Y input terminal of multiplier A3; the output of multiplier A3 is connected to the negative input terminal of operational amplifier U3A through resistor R7; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3A through capacitor C2; the output terminal of operational amplifier U3A outputs a y signal; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U4A through resistor R9; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U2A in the first channel circuit through resistor R3; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3A in the second channel circuit through resistor R6; The output of U3A is connected to the two input terminals of the multiplier A5 in the third channel circuit; the positive input terminal of the operational amplifier U3A is grounded; the positive power supply terminal of the operational amplifier U3A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U3A is connected to the DC voltage source VDD; the output of the operational amplifier U4A is connected to the negative input terminal of the operational amplifier U4A through the resistor R10; the output terminal of the operational amplifier U4A outputs a -y signal; the output of the operational amplifier U4A is connected to the X input terminal of the multiplier A3 in the second channel circuit; the positive input terminal of the operational amplifier U4A is grounded; the positive power supply terminal of the operational amplifier U4A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U4A is connected to the DC voltage source VDD;

[0013] (5) The output of multiplier A4 in the third channel circuit is connected to the Y input terminal of multiplier A6; the output of multiplier A5 is connected to the X input terminal of multiplier A7; the output of multiplier A6 is connected to the negative input terminal of operational amplifier U5A through resistor R12; the output of multiplier A7 is connected to the negative input terminal of operational amplifier U5A through resistor R11; the output of operational amplifier U5A is connected to the negative input terminal of operational amplifier U5A through capacitor C3; the output terminal of operational amplifier U5A outputs a z signal; the output of operational amplifier U5A is connected to the negative input terminal of operational amplifier U6A through resistor R14; the output of operational amplifier U5A is connected to the two input terminals of multiplier A1 in the first channel circuit; the output of operational amplifier U5A is connected to the two input terminals of multiplier A8 in the second channel circuit; the output of operational amplifier U5A is connected to the two input terminals of multiplier A8 in the second channel circuit; The output of U5A is connected to the X input terminal of the multiplier A6 in the third channel circuit; the output of the operational amplifier U5A is connected to the Y input terminal of the multiplier A7 in the third channel circuit; the positive input terminal of the operational amplifier U5A is grounded; the positive power supply terminal of the operational amplifier U5A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U5A is connected to the DC voltage source VDD; the output of the operational amplifier U6A is connected to the negative input terminal of the operational amplifier U6A through the resistor R15; the output terminal of the operational amplifier U6A outputs a -z signal; the output of the operational amplifier U6A is connected to the negative input terminal of the operational amplifier U5A in the third channel circuit through the resistor R13; the positive input terminal of the operational amplifier U6A is grounded; the positive power supply terminal of the operational amplifier U6A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U6A is connected to the DC voltage source VDD.

[0014] 2. According to claim 1, a three-dimensional conservative chaotic system containing dissipative terms but no external force terms is characterized in that: the models of the operational amplifiers U1A, U2A, U3A, U4A, U5A, and U6A are all LF347N.

[0015] 3. A three-dimensional conservative chaotic system with dissipative terms but no external force terms according to claim 1, characterized in that: the models of the multipliers A1, A2, A3, A4, A5, A6, A7, and A8 are all AD633.

[0016] 4. A three-dimensional conservative chaotic system with dissipative terms but no external force terms according to claim 1, characterized in that: the DC voltage source VCC is 15V and VDD is -15V.

[0017] 5. A three-dimensional conservative chaotic system with dissipative terms but no external force terms according to claim 1, characterized in that the capacitance values ​​of the capacitors C1, C2, and C3 are all 10nF.

[0018] 6. According to claim 1, a three-dimensional conservative chaotic system with dissipative terms but no external force terms is characterized in that: the resistance values ​​of the resistors R1, R6, and R13 are all 200kΩ; the resistance values ​​of the resistors R2, R7, and R12 are all 1kΩ; the resistance values ​​of the resistors R3 and R8 are all 666kΩ; the resistance values ​​of the resistors R4, R5, R9, R10, R14, and R15 are all 10kΩ; the resistance value of the resistor R11 is 4kΩ.

[0019] After adopting the above scheme, the present invention is provided with three channel circuits, the input ends and output ends of the three channel circuits are connected to each other, forming a three-dimensional conservative chaotic system with dissipative terms but no external force terms. The circuit has the following beneficial effects:

[0020] (1) The circuit structure is simple and easy to implement;

[0021] (2) The circuit contains only dissipation terms but no external force terms;

[0022] (3) Circuits can generate conservative chaos. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a circuit diagram of the present invention.

[0024] Figure 2 It is the XY phase diagram of the present invention.

[0025] Figure 3 It is the XZ phase diagram of the present invention.

[0026] Figure 4 It is the YZ phase diagram of the present invention. DETAILED DESCRIPTION

[0027] The technical solutions and beneficial effects of the present invention are described in detail below in conjunction with the accompanying drawings. Figure 1-Figure 4 .

[0028] 1. The present invention proposes a three-dimensional conservative chaotic system with dissipative terms but no external force terms. The system has a total of 9 terms, including 5 first-order terms and 4 third-order terms.

[0029] (1) The conservative chaotic system model involved in the present invention is as follows:

[0030]

[0031] Where x, y, z are state variables.

[0032] (2) Figure 1As shown, the simulation circuit involved in the present invention is composed of three channel circuits: the first channel circuit is composed of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U1A, an operational amplifier U2A, a resistor R1, a resistor R2, a resistor R3, a resistor R4, a resistor R5, a multiplier A1, a multiplier A2, a capacitor C1 and an analog ground; the second channel circuit is composed of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U3A, an operational amplifier U4A, a resistor R6, a resistor R7, a resistor R8, a resistor R9, a resistor R10, a multiplier A8, a multiplier A3, a capacitor C2 and an analog ground; the third channel circuit is composed of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U5A, an operational amplifier U6A, a resistor R11, a resistor R12, a resistor R13, a resistor R14, a resistor R15, a multiplier A4, a multiplier A5, a multiplier A6, a multiplier A7, a capacitor C3 and an analog ground;

[0033] (3) The output of the multiplier A1 in the first channel circuit is connected to the X input terminal of the multiplier A2; the output of the multiplier A2 is connected to the negative input terminal of the operational amplifier U2A through the resistor R2; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U2A through the capacitor C1; the output terminal of the operational amplifier U2A outputs the x signal; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U1A through the resistor R4; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U2A in the first channel circuit through the resistor R1; the output of the operational amplifier U2A is connected to the two input terminals of the multiplier A4 in the third channel circuit; the positive input terminal of the operational amplifier U2A The terminal is grounded; the positive power supply terminal of the operational amplifier U2A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U2A is connected to the DC voltage source VDD; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U1A through the resistor R5; the output terminal of the operational amplifier U1A outputs a -x signal; the output of the operational amplifier U1A is connected to the Y input terminal of the multiplier A2 in the first channel circuit; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U3A in the second channel circuit through the resistor R8; the positive input terminal of the operational amplifier U1A is grounded; the positive power supply terminal of the operational amplifier U1A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U1A is connected to the DC voltage source VDD;

[0034] (4) The output of multiplier A8 in the second channel circuit is connected to the Y input terminal of multiplier A3; the output of multiplier A3 is connected to the negative input terminal of operational amplifier U3A through resistor R7; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3A through capacitor C2; the output terminal of operational amplifier U3A outputs a y signal; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U4A through resistor R9; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U2A in the first channel circuit through resistor R3; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3A in the second channel circuit through resistor R6; The output of U3A is connected to the two input terminals of the multiplier A5 in the third channel circuit; the positive input terminal of the operational amplifier U3A is grounded; the positive power supply terminal of the operational amplifier U3A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U3A is connected to the DC voltage source VDD; the output of the operational amplifier U4A is connected to the negative input terminal of the operational amplifier U4A through the resistor R10; the output terminal of the operational amplifier U4A outputs a -y signal; the output of the operational amplifier U4A is connected to the X input terminal of the multiplier A3 in the second channel circuit; the positive input terminal of the operational amplifier U4A is grounded; the positive power supply terminal of the operational amplifier U4A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U4A is connected to the DC voltage source VDD;

[0035] (5) The output of multiplier A4 in the third channel circuit is connected to the Y input terminal of multiplier A6; the output of multiplier A5 is connected to the X input terminal of multiplier A7; the output of multiplier A6 is connected to the negative input terminal of operational amplifier U5A through resistor R12; the output of multiplier A7 is connected to the negative input terminal of operational amplifier U5A through resistor R11; the output of operational amplifier U5A is connected to the negative input terminal of operational amplifier U5A through capacitor C3; the output terminal of operational amplifier U5A outputs a z signal; the output of operational amplifier U5A is connected to the negative input terminal of operational amplifier U6A through resistor R14; the output of operational amplifier U5A is connected to the two input terminals of multiplier A1 in the first channel circuit; the output of operational amplifier U5A is connected to the two input terminals of multiplier A8 in the second channel circuit; the output of operational amplifier U5A is connected to the two input terminals of multiplier A8 in the second channel circuit; The output of U5A is connected to the X input terminal of the multiplier A6 in the third channel circuit; the output of the operational amplifier U5A is connected to the Y input terminal of the multiplier A7 in the third channel circuit; the positive input terminal of the operational amplifier U5A is grounded; the positive power supply terminal of the operational amplifier U5A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U5A is connected to the DC voltage source VDD; the output of the operational amplifier U6A is connected to the negative input terminal of the operational amplifier U6A through the resistor R15; the output terminal of the operational amplifier U6A outputs a -z signal; the output of the operational amplifier U6A is connected to the negative input terminal of the operational amplifier U5A in the third channel circuit through the resistor R13; the positive input terminal of the operational amplifier U6A is grounded; the positive power supply terminal of the operational amplifier U6A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U6A is connected to the DC voltage source VDD.

[0036] 2. In the three channel circuits, the models of operational amplifiers U1A, U2A, U3A, U4A, U5A, and U6A are all LF347N; the models of multipliers A1, A2, A3, A4, A5, A6, A7, and A8 are all AD633; the DC voltage sources VCC are all 15V, and VDD are all -15V; the capacitance values ​​of capacitors C1, C2, and C3 are all 10nF; the resistance values ​​of resistors R1, R6, and R13 are all 200kΩ; the resistance values ​​of resistors R2, R7, and R12 are all 1kΩ; the resistance values ​​of resistors R3 and R8 are all 666kΩ; the resistance values ​​of resistors R4, R5, R9, R10, R14, and R15 are all 10kΩ; the resistance value of resistor R11 is 4kΩ.

[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 ordinary technicians in this technical field within the essential scope of the invention also fall within the protection scope of the invention.

Claims

1. A three-dimensional conservative chaotic system with dissipative terms but no external force terms, characterized in that: (1) A three-dimensional conservative chaotic system (i) with dissipative terms but no external force terms is: Where x, y, z are state variables; (2) A circuit constructed based on system (i), which consists of three channel circuits: The first channel circuit is composed of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U1A, an operational amplifier U2A, a resistor R1, a resistor R2, a resistor R3, a resistor R4, a resistor R5, a multiplier A1, a multiplier A2, a capacitor C1 and an analog ground; the second channel circuit is composed of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U3A, an operational amplifier U4A, a resistor R6, a resistor R7, a resistor R8, a resistor R9, a resistor R10, a multiplier A8, a multiplier A3, a capacitor C2 and an analog ground; the third channel circuit is composed of a DC voltage source VCC, a DC voltage source VDD, an operational amplifier U5A, an operational amplifier U6A, a resistor R11, a resistor R12, a resistor R13, a resistor R14, a resistor R15, a multiplier A4, a multiplier A5, a multiplier A6, a multiplier A7, a capacitor C3 and an analog ground; (3) The output of the multiplier A1 in the first channel circuit is connected to the X input terminal of the multiplier A2; the output of the multiplier A2 is connected to the negative input terminal of the operational amplifier U2A through the resistor R2; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U2A through the capacitor C1; the output terminal of the operational amplifier U2A outputs the x signal; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U1A through the resistor R4; the output of the operational amplifier U2A is connected to the negative input terminal of the operational amplifier U2A in the first channel circuit through the resistor R1; the output of the operational amplifier U2A is connected to the two input terminals of the multiplier A4 in the third channel circuit; the positive input terminal of the operational amplifier U2A The terminal is grounded; the positive power supply terminal of the operational amplifier U2A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U2A is connected to the DC voltage source VDD; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U1A through the resistor R5; the output terminal of the operational amplifier U1A outputs a -x signal; the output of the operational amplifier U1A is connected to the Y input terminal of the multiplier A2 in the first channel circuit; the output of the operational amplifier U1A is connected to the negative input terminal of the operational amplifier U3A in the second channel circuit through the resistor R8; the positive input terminal of the operational amplifier U1A is grounded; the positive power supply terminal of the operational amplifier U1A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U1A is connected to the DC voltage source VDD; (4) The output of multiplier A8 in the second channel circuit is connected to the Y input terminal of multiplier A3; the output of multiplier A3 is connected to the negative input terminal of operational amplifier U3A through resistor R7; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3A through capacitor C2; the output terminal of operational amplifier U3A outputs a y signal; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U4A through resistor R9; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U2A in the first channel circuit through resistor R3; the output of operational amplifier U3A is connected to the negative input terminal of operational amplifier U3A in the second channel circuit through resistor R6; The output of U3A is connected to the two input terminals of the multiplier A5 in the third channel circuit; the positive input terminal of the operational amplifier U3A is grounded; the positive power supply terminal of the operational amplifier U3A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U3A is connected to the DC voltage source VDD; the output of the operational amplifier U4A is connected to the negative input terminal of the operational amplifier U4A through the resistor R10; the output terminal of the operational amplifier U4A outputs a -y signal; the output of the operational amplifier U4A is connected to the X input terminal of the multiplier A3 in the second channel circuit; the positive input terminal of the operational amplifier U4A is grounded; the positive power supply terminal of the operational amplifier U4A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U4A is connected to the DC voltage source VDD; (5) The output of multiplier A4 in the third channel circuit is connected to the Y input terminal of multiplier A6; the output of multiplier A5 is connected to the X input terminal of multiplier A7; the output of multiplier A6 is connected to the negative input terminal of operational amplifier U5A through resistor R12; the output of multiplier A7 is connected to the negative input terminal of operational amplifier U5A through resistor R11; the output of operational amplifier U5A is connected to the negative input terminal of operational amplifier U5A through capacitor C3; the output terminal of operational amplifier U5A outputs a z signal; the output of operational amplifier U5A is connected to the negative input terminal of operational amplifier U6A through resistor R14; the output of operational amplifier U5A is connected to the two input terminals of multiplier A1 in the first channel circuit; the output of operational amplifier U5A is connected to the two input terminals of multiplier A8 in the second channel circuit; the output of operational amplifier U5A is connected to the two input terminals of multiplier A8 in the second channel circuit; The output of U5A is connected to the X input terminal of the multiplier A6 in the third channel circuit; the output of the operational amplifier U5A is connected to the Y input terminal of the multiplier A7 in the third channel circuit; the positive input terminal of the operational amplifier U5A is grounded; the positive power supply terminal of the operational amplifier U5A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U5A is connected to the DC voltage source VDD; the output of the operational amplifier U6A is connected to the negative input terminal of the operational amplifier U6A through the resistor R15; the output terminal of the operational amplifier U6A outputs a -z signal; the output of the operational amplifier U6A is connected to the negative input terminal of the operational amplifier U5A in the third channel circuit through the resistor R13; the positive input terminal of the operational amplifier U6A is grounded; the positive power supply terminal of the operational amplifier U6A is connected to the DC voltage source VCC; the negative power supply terminal of the operational amplifier U6A is connected to the DC voltage source VDD.

2. A three-dimensional conservative chaotic system with dissipative terms but no external force terms according to claim 1, characterized in that: The operational amplifiers U1A, U2A, U3A, U4A, U5A and U6A are all of model LF347N.

3. A three-dimensional conservative chaotic system with dissipative terms but no external force terms according to claim 1, characterized in that: The models of the multipliers A1, A2, A3, A4, A5, A6, A7 and A8 are all AD633.

4. A three-dimensional conservative chaotic system with dissipative terms but no external force terms according to claim 1, characterized in that: The DC voltage sources VCC and VDD are both 15V and -15V, respectively.

5. A three-dimensional conservative chaotic system with dissipative terms but no external force terms according to claim 1, characterized in that: The capacitance values ​​of the capacitors C1, C2 and C3 are all 10 nF.

6. A three-dimensional conservative chaotic system with dissipative terms but no external force terms according to claim 1, characterized in that: The resistance values ​​of the resistors R1, R6, and R13 are all 200kΩ; the resistance values ​​of the resistors R2, R7, and R12 are all 1kΩ; the resistance values ​​of the resistors R3 and R8 are all 666kΩ; the resistance values ​​of the resistors R4, R5, R9, R10, R14, and R15 are all 10kΩ; and the resistance value of the resistor R11 is 4kΩ.

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