A three-dimensional Hindmarsh-Rose neuron model circuit under periodic excitation

Abstract

The application discloses a three-dimensional Hindmarsh-Rose neuron model circuit under periodic excitation, comprising three neuron circuits and a matching circuit, and is composed of nine operational amplifiers and two multiplier circuits. The three-dimensional Hindmarsh-Rose neuron model circuit under periodic excitation can provide hardware support for studying neuron dynamic behaviors under periodic excitation, and has important theoretical research significance and practical application value.

Description

Technical Field

[0001] The present invention belongs to the technical field of neuron model circuits, and in particular relates to a three-dimensional Hindmarsh-Rose neuron model circuit. Background Art

[0002] Neuroscience research has only been around for a century. Because neurons are the fundamental units of the nervous system, previous research has been based on neuronal models. Neurons number in the mammalian nervous system, reaching billions. When the human brain transmits information, neurons emit electrical discharges and transmit information between neurons. This allows the body to sense changes in the external environment, transmit the brain's signals in response to these changes, and thus interact with the external environment. To understand the workings of the nervous system, many researchers have developed various mathematical models to describe the firing behavior of neurons. Currently, a wide variety of neuronal models exist. Over the past three decades, numerous models have evolved from the classic Hodgkin-Huxley model to describe the firing dynamics of neurons, such as the FitzHugh-Naguma model, the Hindmarsh-Rose model, and the Morris-Lecar model.

[0003] In 1984, Hindmarsh and Rose proposed the Hindmarsh-Rose (HR) neuron model. As a generalization of the FHN model, the HR model can better explain the dynamic characteristics of neurons, such as pulse discharge, cluster discharge, and chaotic behavior. This model has a relatively sensitive response characteristic to the excitation of the system. For the research direction of rotating machinery bearing fault diagnosis, by constructing a reasonable system model, utilizing the unique sensitivity to external excitation and excellent noise resistance of Hindmarsh-Rose neurons (neurodynamic systems), combined with signal processing methods such as empirical mode decomposition and fractal dynamics, by extracting the characteristics of weak signals instead of eliminating or suppressing noise, the singular characteristics of bearing damage in vibration information can be identified, thereby providing a theoretical basis for the bearing damage judgment criteria of the neurodynamic system under weak signal excitation.

[0004] Considering that neuron models are generally composed of second-order or third-order mutually coupled differential equations, and as the number of neurons increases, the computational load for dynamic analysis will also be very huge, so the real-time performance of the analysis and calculation cannot be guaranteed. Summary of the Invention

[0005] In order to overcome the prior art, the present application provides a three-dimensional Hindmarsh-Rose neuron model circuit under periodic excitation, comprising three neuron circuits and a matching circuit, which is composed of 9 operational amplifiers and 2 multiplier circuits, can provide hardware support for studying the dynamic behavior of neurons under periodic excitation, and has important theoretical research significance and practical application value.

[0006] The technical solution adopted by the present application to solve its technical problems comprises the following steps:

[0007] A three-dimensional Hindmarsh-Rose neuron model circuit under periodic excitation, according to Kirchhoff's law and the electrical characteristics of circuit components, the circuit equation is as follows:

[0008]

[0009] Wherein, X, Y, Z represent the output of neuron circuit X, neuron circuit Y, and neuron circuit Z in the three-dimensional Hindmarsh-Rose neuron model circuit respectively; R1 to R 27 All represent resistors, ui represents the periodic excitation input at U2, V cc represents the input of neuron circuit Y and neuron circuit Z, which is set to a direct current excitation of 9V; C1 to C3 represent capacitors;

[0010]

[0011]

[0012]

[0013]

[0014] The specific circuit is described as follows:

[0015] The periodic excitation ui of the neuron model circuit is input into the neuron model circuit after being divided by the voltage dividing circuit composed of resistors R9 and R 10 connected to the positive input end of operational amplifier U2, and U2 is an input isolator; the periodic excitation is input into the positive input end of operational amplifier U1 through resistor R8 after being isolated by U2, U1 is a same-phase proportional operational circuit, resistors R4 to R8 are connected to the positive input end of U1; the output of U1 and resistor R 11 are connected in series, and the output is the output of neuron circuit X; one end of capacitor C1 is connected to resistor R 11 , and the other end is grounded; resistors R1, R2, and R3 are connected to the inverting input end of U1; the other end of resistor R2 is grounded; the other end of resistor R1 is connected to the output of U1; the inverting input end and the output of U2 are directly connected;

[0016] The input voltage of neuron circuit Y is V cc , by the resistor R 15 、R 16 The voltage divider circuit formed by the voltage divider is input into the positive input terminal of the operational amplifier U4, and then output by U4 and then pass through the resistor R 17 、R 18 The voltage divider circuit is divided and input to the positive input terminal of the operational amplifier U3; the output terminal of U3 is connected to the resistor R 19 The output of neuron circuit Y is connected in series; one end of capacitor C2 is connected to resistor R 19 connected, and the other end is grounded; the inverting input and output of U4 are directly connected; the resistor R 14 One end is connected to the resistor R7, and the other end is connected to the positive input terminal of U3; 13 and R 12 Connected to the inverting input of U3; resistor R 12 The other end is connected to the output of U3 and R 19 Series connection; resistance R 13 Connect the other end to R5;

[0017] The input voltage of neuron circuit Z is set to 9V, and the 24 、R 25 The voltage divider circuit is divided and input to the operational amplifier U6, and then output by U6 and then through R 23 、R 26 The voltage divider circuit formed by the voltage divider is input to the positive input terminal of U5 after voltage division; the output terminal of U5 is connected to the resistor R 27 The output of the neuron circuit Z is connected in series; one end of the capacitor C3 is connected to the resistor R 27 connected, and the other end is grounded; the inverting input and output of U6 are directly connected; the resistor R 22 One end is connected to the output of neuron circuit X and the positive input of U5, and the other end is connected to the output of neuron circuit X; resistor R 21 and R 20 Connected to the inverting input of U5; resistor R 20 The other end is connected to the output of U5; the resistor R 21 The other end is grounded;

[0018] The output of neuron circuit X is connected to the non-inverting input terminal of operational amplifier U1 after passing through resistor R4; the output of neuron circuit X serves as two inputs of the square operator and one input of the inverting cube operator; the output of neuron circuit Y is connected to the non-inverting input terminal of operational amplifier U1 after passing through resistor R7; the output of neuron circuit Z is connected to the inverting input terminal of operational amplifier U1 after passing through resistor R3 to form coupling between neuron circuits;

[0019] The output of the squaring operator is connected to the positive input terminal of the operational amplifier U1 through a resistor R5; and the output of the inverting cubic operation circuit is connected to the positive input terminal of the operational amplifier U1 through a resistor R6.

[0020] Further, the output interface of the neuron model circuit can be connected to a load, specifically as follows:

[0021] The output of the neuron circuit X is connected to the positive input terminal of the operational amplifier U9, and the input and output are isolated; the output of U9 is connected to the inverting input terminal of the operational amplifier U10 through a resistor RX2, and is connected to the load LEDX after being inversely and proportionally amplified by U10, thereby driving the load LEDX; RX1, RX2, RX3, RX4 and RX5 are proportional resistors; the inverting input terminal of the operational amplifier U9 is connected to the resistor RX1; and the positive input terminal of the operational amplifier U10 is connected to the resistor RX5.

[0022] The output of the neuron circuit Y is similar to that of the neuron circuit X, and is first isolated by the operational amplifier U7, then is inversely connected by the operational amplifier U8, and then is connected to the load LEDY; for the output of the neuron circuit Z, because the output voltage can drive the load, the output is only isolated and then connected to the load LEDZ.

[0023] The beneficial effects of the present application are as follows:

[0024] The circuit of the present application has simple and clear structure, and the components used are cheap, simple and easy to find, and easy for researchers to test and analyze, and the circuit is easy to integrate. In the circuit, when the input is periodic excitation, the output characteristic is good, which shows that when the Hindmarsh-Rose neuron is excited by alternating current, complex neural dynamic behavior is generated, and it has great research significance for studying the spiking, bursting and other discharge behaviors of the Hindmarsh-Rose neuron. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 is a schematic diagram of the neuron model circuit of the present application.

[0026] Figure 2 is the simulation software output waveform diagram and X-Y phase diagram of X and Y after X input alternating current excitation of the embodiment of the present application, (a) simulation software output waveform diagram, (b) X-Y phase diagram.

[0027] Figure 3 is the actual output diagram and X-Y phase diagram of X and Y after X input alternating current excitation of the embodiment of the present application, (a) actual output diagram, (b) X-Y phase diagram.

[0028] Figure 41. The actual output diagram of Y and Z and the YZ phase diagram after AC excitation of X input in the embodiment of the present invention, (a) actual output diagram, (b) XY phase diagram.

[0029] Figure 5 1. The actual output diagram of X and Z and the XZ phase diagram after AC excitation is input to X in the embodiment of the present invention, (a) actual output diagram, (b) XY phase diagram. DETAILED DESCRIPTION

[0030] The present invention will be further described below with reference to the accompanying drawings and examples.

[0031] In order to solve the problem of real-time dynamic analysis of neuron models, this paper proposes a three-dimensional Hindmarsh-Rose neuron model circuit under periodic excitation based on the characteristics of low hardware circuit cost, good real-time performance and easy integration. It provides hardware support for studying the dynamic behavior of neurons under periodic excitation, which has important theoretical research significance and practical application value.

[0032] The technical solution adopted by the present invention is to design a three-dimensional Hindmarsh-Rose neuron model circuit under periodic excitation and build a corresponding hardware circuit, the structure of which is as follows:

[0033] The circuit is: a three-dimensional Hindmarsh-Rose neuron model under periodic excitation to realize the circuit diagram, such as Figure 1 The three-dimensional Hindmarsh-Rose neuron model implementation circuit includes a neuron model circuit and an output isolation circuit.

[0034] The neuron model implementation circuit consists of 9 operational amplifiers and 2 multiplier circuits. Figure 1 In the figure, the periodic excitation ui is input into the neuron circuit model by a voltage divider circuit composed of R9 and R10 connected to the non-inverting input of the operational amplifier U2. The specific voltage divider ratio can be controlled by R9 and R10. U2 is an input isolator. After being isolated by U2, the periodic excitation is input from the output end through R8 to the non-inverting input of the operational amplifier U1. U1 is a non-inverting proportional operational circuit. R4, R5, R6, R7, and R8 are connected to the non-inverting input of U1. Their values ​​are related to the coefficients of the equation. See formulas (5) and (6) for details. The output of U1 is connected in series with R11 to become the output of X. The capacitors C1 and R11 connected to R11 are used as coefficients in the equation.

[0035] Similarly, the input of Y has been set to 9V in this neuron circuit, and R 15 、R 16 The voltage divider circuit is divided and input to the positive input terminal of U4, and then output by U4 and then pass through R 17 、R 18The voltage divider circuit is divided and input to the positive input terminal of the operational amplifier U3. The output terminal of U3 is output through R, which is the output of Y in the neuron circuit. The same C2, R 19 The coefficients of the equation are shown in formulas (5) and (6).

[0036] The input of neuron circuit Z is similar to that of Y. The input voltage is also fixed to 9V in the present invention. 24 、R 25 The voltage divider circuit is divided and input to the operational amplifier U6, and then output by U6 and then through R 23 、R 26 The voltage divider circuit formed by the voltage divider is input to the positive input terminal of U5 after voltage division. The output of U5 is the output of Z. C3, R 11 is the coefficient of the equation, see formula (5) and (6) for details.

[0037] In this circuit, the output of X is connected to the non-inverting input of operational amplifier U1 via R4. The output of X serves as the input of the square multiplier circuit and is connected to the non-inverting input of operational amplifier U5 via R22. The output of Y is connected to the non-inverting input of operational amplifier U1 via R7. The output of Z is connected to the inverting input of operational amplifier U1 via R3.

[0038] To meet the computational requirements of this circuit, a squaring circuit and an inverting cubing circuit are also required. To achieve this, this circuit connects the input and output of the squaring circuit to another squaring circuit to achieve the inverting cubing operation. Furthermore, to meet the equation's requirements, this neuron circuit connects the output of the squaring circuit to the non-inverting input of operational amplifier U1 via R5; and the output of the inverting cubing circuit to the non-inverting input of operational amplifier U1 via R6.

[0039] In the present invention, a peripheral circuit is also designed that can connect a certain load (the specific load in the present invention is an LED lamp) to the X, Y, and Z output interfaces respectively without affecting the output characteristics of the original neuron circuits X, Y, and Z. For the output of X, it is connected to the operational amplifier U9, and the input and output are first isolated. The output of U9 is connected to U10. After being amplified by U10 inversely, it is connected to LEDX to drive the load. RX1, RX2, RX3, RX4, and RX5 are matching resistors. For the output of Y, similar to X, an isolator is still first constructed through the operational amplifier U7, and the output characteristics of Y are inverted. Then, the load LEDY is connected. RY1, RY2, RY3, RY4, and RY5 are corresponding matching resistors. For the output of Z, because its output voltage is sufficient to drive the load, it is only necessary to isolate it and then output it. RZ1 and RZ2 are matching resistors.

[0040] Mathematical Modeling: This invention implements a three-dimensional Hindmarsh-Rose neuron model circuit under periodic excitation. This circuit is based on a three-dimensional Hindmarsh-Rose neuron, whose system equation contains three state variables x, y, and z. By modifying its circuit structure, its output characteristics under periodic input excitation have theoretical research significance. The model can be described by three coupled first-order ordinary differential equations:

[0041]

[0042] Where x is the membrane potential, y is the peak variable used to measure the rate at which Na+ and K+ pass through the fast channel, and z is the burst variable, which represents the rate at which other ions pass through the slow channel. When the parameters in the equation are varied, the model can reproduce the burst discharge, peak discharge, or chaotic activity of real biological neurons. In the present invention, the parameters are a = 1.0, b = 3.0, c = 1.0, d = 5.0, r = 0.0021, s = 4.0, and χ = -1.60. Here, Iext is expressed as follows:

[0043] I ext =I+Q0 cosωt (2)

[0044] Where I is the direct bias component of the external excitation, Q0 is the excitation amplitude, and ω is the excitation frequency.

[0045] exist Figure 1 In a three-dimensional Hindmarsh-Rose neuron circuit under periodic excitation shown in , considering the limitations of nonlinear analog components in the circuit, the scaling of formula (3) is adopted as follows:

[0046]

[0047] The scaled equivalent system is governed by the following equations:

[0048]

[0049] According to Kirchhoff's law and the electrical characteristics of circuit components, the relevant circuit equations of the Hindmarsh-Rose circuit model are as follows (ui is the periodic excitation input of the actual circuit, V cc Set to 9V):

[0050]

[0051] in:

[0052]

[0053] In the above equation, the specific parameters of each component are shown in Table 1:

[0054] Table 1 Component parameters

[0055]

[0056] The final output is shown in Figure 2 、 Figure 3 、 Figure 4 、 Figure 5 , where the AC excitation parameters of the final result are:

[0057] Amplitude: 3.5V, DC bias: 6.5V, frequency: 100Hz (different excitation parameters will result in different circuit outputs)

[0058] Thus, the present invention has constructed a circuit implementation scheme of a three-dimensional Hindmarsh-Rose neuron model under periodic excitation.

Claims

1. A three-dimensional Hindmarsh-Rose neuron model circuit under periodic excitation, characterized in that: According to Kirchhoff's law and the electrical characteristics of circuit components, the circuit equation is expressed as follows: Among them, X, Y, and Z represent the outputs of neuron circuit X, neuron circuit Y, and neuron circuit Z in the three-dimensional Hindmarsh-Rose neuron model circuit respectively; R1 to R 27 All represent resistance, ui represents the periodic excitation input at U2, V cc represents the input of neuron circuit Y and neuron circuit Z, which is set to a DC excitation of 9V; C1 to C3 represent capacitors; The specific circuit description is as follows: The periodic excitation ui of the neuron model circuit is connected to the resistor R9 and R 10 The voltage divider circuit is divided and input into the neuron model circuit. U2 is the input isolator. The periodic excitation is isolated by U2 and then input from the output end to the positive input end of the operational amplifier U1 through the resistor R8. U1 is a non-inverting proportional operational circuit. The resistors R4 to R8 are connected to the positive input end of U1. The output of U1 is connected to the resistor R 11 The output of neuron circuit X is connected in series; one end of capacitor C1 is connected to resistor R 11 The other end of resistor R1, R2, and R3 are connected to the inverting input of U1; the other end of resistor R2 is grounded; the other end of resistor R1 is connected to the output of U1; the inverting input and output of U2 are directly connected; The input voltage of neuron circuit Y is V cc , by the resistor R 15 、R 16 The voltage divider circuit is divided and input into the positive input terminal of the operational amplifier U4, and then output by U4 and then through the resistor R 17 、R 18 The voltage divider circuit is divided and input to the positive input terminal of the operational amplifier U3; the output terminal of U3 is connected to the resistor R 19 The output of neuron circuit Y is connected in series; one end of capacitor C2 is connected to resistor R 19 connected, and the other end is grounded; the inverting input and output of U4 are directly connected; the resistor R 14 One end is connected to the resistor R7, and the other end is connected to the positive input terminal of U3; 13 and R 12 Connected to the inverting input of U3; resistor R 12 The other end is connected to the output of U3 and R 19 Series connection; resistance R 13 Connect the other end to R5; The input voltage of neuron circuit Z is set to 9V, and the 24 、R 25 The voltage divider circuit is divided and input to the operational amplifier U6, and then output by U6 and then through R 23 、R 26 The voltage divider circuit is divided and input to the positive input terminal of U5; the output terminal of U5 is connected to the resistor R 27 The output of the neuron circuit Z is connected in series; one end of the capacitor C3 is connected to the resistor R 27 connected, and the other end is grounded; the inverting input and output of U6 are directly connected; the resistor R 22 One end is connected to the output of neuron circuit X and the positive input of U5, and the other end is connected to the output of neuron circuit X; resistor R 21 and R 20 Connected to the inverting input of U5; resistor R 20 The other end is connected to the output of U5; the resistor R 21 The other end is grounded; The output of neuron circuit X is connected to the non-inverting input terminal of operational amplifier U1 after passing through resistor R4; the output of neuron circuit X serves as two inputs of the square operator and one input of the inverting cube operator; the output of neuron circuit Y is connected to the non-inverting input terminal of operational amplifier U1 after passing through resistor R7; the output of neuron circuit Z is connected to the inverting input terminal of operational amplifier U1 after passing through resistor R3 to form coupling between neuron circuits; The output of the square operator is connected to the non-inverting input terminal of the operational amplifier U1 through the resistor R5; the output of the inverting cubic operation circuit is connected to the non-inverting input terminal of the operational amplifier U1 through the resistor R6.

2. The three-dimensional Hindmarsh-Rose neuron model circuit under periodic excitation according to claim 1, characterized in that: The output interface of the neuron model circuit can be connected to a load, specifically as follows: The output of neuron circuit X is connected to the positive input of operational amplifier U9 to isolate the input and output. The output of U9 is connected to the negative input of operational amplifier U10 via resistor RX2. After being inverted and proportionally amplified by U10, it is connected to load LEDX, thus driving load LEDX. RX1, RX2, RX3, RX4, and RX5 are matching resistors. The negative input of operational amplifier U9 is connected to resistor RX1. The positive input of operational amplifier U10 is connected to resistor RX5. The output of neuron circuit Y is similar to that of neuron circuit X. An isolator is first constructed through operational amplifier U7, then inverted through operational amplifier U8, and finally connected to the load LEDY. As for the output of neuron circuit Z, since its output voltage can drive the load, it is only isolated and then output to the load LEDZ.

Images