Novel discrete memristor coupling heterogeneous neuron model construction method and application

Abstract

The invention discloses a novel discrete memristor coupling heterogeneous neuron model construction method and application, and designs a novel discrete memristor model to simulate two different neuron models of synaptic coupling to obtain a final novel discrete memristor coupling heterogeneous neuron model. A phase diagram, an iterative sequence, a bifurcation diagram, a Lyapunov exponential spectrum and other methods are used for analyzing the dynamic characteristics of the model, and it is found that the model presents rich dynamic behaviors such as hyper-chaos, chaos and periods and a neuron discharge mode. The high complexity shows that the novel discrete memristor coupling heterogeneous neuron model can be applied to the security field of image encryption and the like. The constructed coupled neuron model is a discrete system, so that the digital circuit of the model is easy to realize through a DSP (Digital Signal Processor). The coupling neuron model-based application to image encryption is good in effect and high in security.

Description

Technical Field

[0001] The present invention belongs to the interdisciplinary field of neuroscience and nonlinear science, and specifically relates to a novel discrete memristor-coupled heterogeneous neuron model construction method and application. Background Art

[0002] Neurons are the fundamental structural and functional units of the biological nervous system. Constructing various neuron models is of great significance for studying the nervous system. Neurons connect through synapses, forming a complex and efficient neural network that maintains normal life. The structure of a synapse consists of a presynaptic membrane, a postsynaptic membrane, and synaptic vesicles. The transfer of neurotransmitters from the presynaptic membrane to the postsynaptic membrane generates an action potential. Memristors offer fast access speeds, low energy consumption, and a compact size. Memristors are nonlinear memory elements that are generally nonvolatile, and their resistance changes with the flow of charge. These characteristics enable memristors to simulate synapses. Incorporating memristors into neuron models can more realistically simulate the workings of neurons.

[0003] Neurons are diverse and possess a rich variety of functions. A synaptic connection between two different neurons is called a heterogeneous neuronal connection. Through experimental analysis, researchers have proposed numerous independent neuronal models. Continuous models include the FitzHugh-Nagumo neuron model and the Hindmarsh-Rose neuron model. Discrete models include the Chialvo neuron model and the Rulkov neuron model. These neuronal models can simulate some simple dynamic behaviors of biological neurons. Neurons exhibit a wide variety of firing patterns and dynamic behaviors when transmitting information. Ion flow within neurons and external stimuli can lead to phenomena such as chaos. Neuronal dynamic behavior is also a dynamic process, and changes in various parameters can affect neuronal firing activity. Neurons are deterministic nonlinear systems, and the memristor coupled neuron model is a more complex nonlinear system. Using nonlinear theories and methods, we can study and analyze the dynamic characteristics of various neuronal models.

[0004] Compared with continuous neuron model, the operation speed of discrete neuron model is faster and more efficient. The discrete neuron model can more efficiently and quickly simulate the complete behavior of biological neurons under low-dimensional conditions. The memristor-coupled heterogeneous neuron model can simulate the working principle of two different neurons connected through synapses, and can obtain more complete neuron firing patterns and dynamic behaviors. At present, the research on discrete memristor-coupled heterogeneous neuron model is less, and the versatility and flexibility are low. Therefore, it is necessary to construct a new type of discrete memristor-coupled heterogeneous neuron model. The discrete nonlinear model capable of generating chaos, also known as discrete chaotic mapping, has high sensitivity to initial values, and the generated chaotic sequence can be applied to image encryption and the like. With the development of digital signal processing technology, the digital circuit implementation of nonlinear systems is a research hotspot. Digital signal processing (DSP) technology is less affected by external factors, has programmability, and is convenient for flexible signal processing. In order to verify the digital circuit implementability of the model, the DSP is used to realize the memristor-coupled heterogeneous neuron model. The CCS platform in the application is Code Composer Studio 6.0.0. SUMMARY

[0005] The purpose of the present application is to solve the problem of the prior art that the research on discrete memristor-coupled heterogeneous neuron model is less, and the versatility and flexibility of the neuron analysis are low.

[0006] In order to solve the above problems, the present application provides a new type of discrete memristor-coupled heterogeneous neuron model construction application, which comprises a memristor construction module, a coupling module, a dynamics analysis module and a DSP construction module.

[0007] In the preferred mode, M1: the implementation of the memristor construction module is as follows:

[0008] Based on the definition of the memristor, the mathematical model of the discrete memristor is obtained, and the formula is as follows:

[0009]

[0010] In the formula, u(n) is the input of the memristor, x(n) is the output of the memristor, z(n) represents the state variable of the memristor, h(·) represents the memduct form of the discrete memristor, and f(·) represents the intermediate state variable expression of the discrete memristor.

[0011] In the preferred mode, M2: the implementation of the coupling module is as follows:

[0012] The synapse is simulated by using the discrete memristor obtained in step M1 to couple two different discrete neuron models F1(·) and F2(·), and a final new type of discrete memristor-coupled heterogeneous neuron model is constructed, and the formula is as follows:

[0013]

[0014] Where x1, y1, x2, y2 are neuron state variables, z is the intermediate state variable of discrete memristor, I ext1 and I ext2 is the external stimulus, h(z(n))(x1(n)-x2(n)) is the discrete memristive synaptic current.

[0015] In the preferred embodiment, M3: Kinetic analysis module is implemented as follows:

[0016] The dynamic characteristics of the new discrete memristor coupled heterogeneous neuron model are analyzed, and the influence of changes in parameters and initial values ​​on the dynamic behavior of the model state variables is studied. Smaller model parameters, that is, initial values ​​less than 5 and close to the origin, are selected to determine appropriate model parameters and initial values ​​for the DSP implementation of the model.

[0017] In the preferred embodiment, the M4: DSP building block is implemented as follows:

[0018] A novel discrete memristor-coupled heterogeneous neuron model is implemented based on DSP. The memristor-coupled neuron model is implemented based on the 32-bit TMS320F2855 chip. The TMS320F2855 chip is connected to a computer via the MAX3232 communication interface and to the UTD7102 oscilloscope via the DAC8552 DA converter. The TMS320F2855 chip is initialized on the CCS platform on the computer and the GPIO port is configured.

[0019] A novel discrete memristor coupled heterogeneous neuron model construction method includes:

[0020] S1: Process the plaintext image I based on the novel discrete memristor coupled heterogeneous neuron model obtained in step M4;

[0021] S1-1: Input plaintext image I and record image height H and width W;

[0022] S1-2: Determine a set of parameters and initial values ​​ε=3.8, kr=-0.1, α=-0.015, β=-0.65, a=2.695, b=0.18, γ=4.8, μ=0.02, σ=-0.2. When the initial value φ0=(-1,-1,0,1,1), iterate the model obtained in step S4 H×W times to obtain four sets of chaotic sequences. The formula is as follows:

[0023]

[0024] Where X, Y, Z, and U are the chaotic sequences of iterative operations of the neuron state variables x1, z, x2, and y2 in the coupled neuron model, floor represents the rounding down operation, and mod represents the modulo operation.

[0025] S1-3: Use the four sets of chaotic sequences generated to perform scrambling operations on the plaintext image I, disrupting the pixel positions to obtain the image I1 after pixel position transformation. The formula is as follows:

[0026]

[0027] Where i and j represent the row and column pixel coordinates of the plaintext image I, ii and jj represent the row and column pixel coordinates of the scrambled image I1, (ii, jj) is the image pixel position after the scrambling operation, and double represents the conversion of floating-point type;

[0028] S1-4: Convert the scrambled image I1 into a vector and perform diffusion operation to change the image pixel value. The formula is as follows:

[0029]

[0030] Where I1(i) is the pixel value of the scrambled image, I2 is the final encrypted image, and I2(i) is the pixel value of the image after conversion to a vector and diffusion operation;

[0031] S1-5: Using a symmetric encryption algorithm, the inverse operation of encryption is performed to decrypt the image. The decrypted image is obtained by performing the inverse diffusion of the formula in S1-4 on I2 and then performing the inverse scrambling of the formula in S1-3.

[0032] The beneficial effects of the present invention are as follows: by simulating synaptic coupling of two different discrete neuron models through memristors, the dimension of the neurons can be one-dimensional, two-dimensional or multi-dimensional. This method is versatile and flexible and can couple any two discrete neuron models. The dynamic characteristics analysis shows that the heterogeneous neuron model constructed by the method of the present invention exhibits complex and diverse discharge patterns and dynamic behaviors; in addition, the complexity analysis shows that the method of the present invention constructs a highly complex coupled neuron model. Then, DSP implementation shows that the memristor coupled neuron model constructed by the present invention can be realized by digital circuits. Finally, the encryption of grayscale images is achieved by combining the chaotic sequence generated by the new discrete memristor coupled heterogeneous neuron model with a simple encryption algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a structural diagram of the new discrete magnetically controlled memristor model constructed;

[0034] Figure 2 is the vi characteristic curve of the memristor model;

[0035] Figure 3 This is a structural diagram of the two-dimensional discrete Chailvo neuron model and the Rulkov neuron model coupled by a memristor;

[0036] Figure 4 is the attractor phase diagram of the discrete memristor coupled heterogeneous neuron model;

[0037] Figure 5 is the memristor coupling parameter k r Bifurcation diagram and Lyapunov exponent spectrum when changing;

[0038] Figure 6 For different coupling parameters k r The attractor phase diagram below;

[0039] Figure 7 is the bifurcation diagram and Lyapunov exponent spectrum when the neuron parameter c changes;

[0040] Figure 8 The attractor phase diagram and neuron discharge pattern under different neuron parameters c;

[0041] Figure 9 is the bifurcation diagram and Lyapunov exponent spectrum when the neuron external effect parameter σ changes;

[0042] Figure 10 is the attractor phase diagram under different neuron external effect parameters σ;

[0043] Figure 11 Various neuronal firing patterns presented for the discrete memristor-coupled heterogeneous neuron model;

[0044] Figure 12 for other neuronal firing patterns;

[0045] Figure 13 is the three-dimensional SE complexity under different parameters;

[0046] Figure 14 Hardware connection diagram for implementing coupled neuron model for DSP;

[0047] Figure 15 A physical representation of the coupled neuron model implemented for DSP;

[0048] Figure 16 Implement result graph for DSP;

[0049] Figure 17 Image encryption and decryption results based on the chaotic sequence generated by the coupled neuron model;

[0050] Figure 18 Performance test results for image encryption. DETAILED DESCRIPTION

[0051] Example 1:

[0052] A novel discrete memristor coupled heterogeneous neuron model construction method includes:

[0053] S1: Based on the definition of memristor, the mathematical model of discrete memristor is obtained;

[0054] The mathematical model of the memristor in S1 is:

[0055]

[0056] Where vn is the memristor input voltage, in is the memristor output current. W(φn) is the memristor derivative, which is composed of a cosine function and a power function, where α and β are memristor parameters. φn is the memristor flux state variable, and h is the memristor internal parameter. The memristor operation structure obtained from the mathematical model is as follows: Figure 1 shown.

[0057] When h=1, a sinusoidal voltage signal vn=Vmsin(ωn) is applied across the memristor. When the initial value of the memristor flux is 0, Figure 2 The vi characteristic curves under different voltage amplitudes (Vm), angular frequencies (ω), and memristor parameters (α, β):

[0058] (a)ω=9, α=-0.35, β=-0.65, (b) Vm=4, α=-0.35, β=-0.65, (c)ω=1, α=-0.35, β=0.65, (d) Vm=0.3, α=-0.35, β=0.65. Figure 2 The area enclosed by the characteristic curve increases with the increase of Vm and decreases with the increase of ω, which means that the designed new discrete memristor model conforms to the basic characteristics of the memristor.

[0059] S2: Use the new discrete magnetically controlled memristor in step S1 to simulate the neural synaptic coupling two-dimensional discrete Chialvo neuron model and Rulkov neuron model to obtain the final new discrete memristor coupled heterogeneous neuron model. The state equation of the model is:

[0060]

[0061] Where f(z(n)) = αcos(πz(n)²) + β, x1 and y1 are the state variables of the Chialvo neuron, x2 and y2 are the state variables of the Rulkov neuron, and z is the flux state variable of the memristor. kr is the memristor coupling parameter, ε, a, b, c are the Chialvo neuron parameters, and μ and σ are the Rulkov neuron parameters. The structure of the coupled neuron model in the formula is shown in the figure below. Figure 3 shown.

[0062] When ε=0.1,kr=0.3,α=-0.35,β=-0.65,a=0.7,b=0.18,γ=4.8,μ=0.01,σ=1.35, and the initial value of the model φ0=(-1,-1,1,1,0), changing the value of parameter c can obtain Figure 4 Different types of hyperchaotic attractors: c = 1.9 for the hyperchaotic attractor: (a) y1-x2 phase plane, (b) x1-y1-x2 phase plane, (c) x1-y1 phase plane; c = 1.45 for the chaotic attractor: (d) y1-x2 phase plane, (e) x1-y1-x2 phase plane, (f) x1-y1 phase plane. When c = 1.9, the Lyapunov exponent spectrum of the model is LE1 = 6.8120, LE2 = 6.4310, LE3 = 0.1030, LE4 = 0, LE5 ​​= -0.5991. When c = 1.45, the Lyapunov exponent spectrum of the model is LE1 = 6.3527, LE2 = 6.3031, LE3 = 0, LE4 = 0, LE5 ​​= -0.5411.

[0063] S3: Analysis of the dynamic characteristics of a novel discrete memristor coupled heterogeneous neuron model;

[0064] The following analysis uses several methods to analyze the dynamic characteristics of this novel discrete memristor coupled heterogeneous neuron model, exploring the influence of different parameters on the dynamic behavior, thereby demonstrating that this coupled neuron model has rich dynamic characteristics. The model's complexity is then calculated under different parameters to determine the complexity of the model's generated sequences.

[0065] For attractors generated by continuous systems or discrete mappings, bifurcation diagrams can reflect the impact of parameter size on the attractor's topological structure. Positive Lyapunov exponents are a fundamental characteristic of chaotic systems, and the Lyapunov exponent spectrum is an important indicator for determining whether a system is in a chaotic state. If there are two or more positive Lyapunov exponents, the system is in a more complex hyperchaotic state. For discrete neuron models, the iterative sequence in which the state table variables change with the number of iterations can reflect the neuron's discharge behavior. Spectral entropy (SE) complexity is also a method for analyzing the dynamic behavior of a system. The larger the complexity value, the closer the chaotic sequence generated by the system is to a pseudo-random sequence.

[0066] Figure 5 The figure shows the dynamic characteristics of the new discrete memristor coupled heterogeneous neuron model when the parameters ε=0.1, α=-0.35, β=-0.65, a=0.695, b=0.18, c=1.75, γ=3.8, μ=0.01, σ=1.5, the model initial value φ0=(-1,-1,1,0,0), and the memristor coupling parameter kr is [-0.1,0.5]. Figure 5The bifurcation diagram in (a) and Figure 5 It can be clearly observed from the Lyapunov exponent spectrum in (b) that, except for the case when kr = 0, the model is in a periodic state. For other values ​​of kr, the system is in a hyperchaotic state, including the cases with two positive Lyapunov exponents and three positive Lyapunov exponents.

[0067] Figure 6 Shown are the phase diagrams of hyperchaotic attractors under different memristor coupling parameters kr: (a) kr = -0.03, (b) kr = 0.1, (c) kr = 0.18, (d) kr = 0.3.

[0068] Figure 7 The figure shows the changes in the dynamic characteristics of the coupled neuron model of the new discrete memristor coupled heterogeneous neuron model when the parameters ε = 0.1, kr = 0.035, α = 0, β = -0.65, a = 0.695, b = 0.18, γ = 3.8, μ = 0.01, σ = 0.25, and the initial value of the model φ0 = (-1, -1, 1, 1, 0), and the neuron parameter c is in [1.4, 2.6]. Figure 7 The bifurcation diagram in (a) and Figure 7 The Lyapunov exponent spectrum in (b) clearly shows the presence of narrow periodic windows as the parameter c increases. Under other conditions, the coupled neuron model is in a chaotic state. Periodic and chaotic states alternate as c changes.

[0069] Figure 8 Shown are the attractor phase diagrams and neuron discharge patterns under different neuron parameters c: (a) periodic attractor with c = -0.03, (b) periodic discharge pattern with c = 2.1, (c) type I chaotic attractor with c = 2.1, (d) type I periodic discharge pattern with c = 2.1, (e) type II chaotic attractor with c = 2.4, and (f) type II chaotic discharge pattern with c = 2.4.

[0070] Figure 9 The figure shows the dynamic characteristics of the new discrete memristor coupled heterogeneous neuron model when the parameters ε=0.1, kr=0.15, α=-0.35, β=-0.65, a=0.7, b=0.18, c=2.1, γ=2, μ=0.01, initial value φ0=(-1,-1,1,1,0), and the neuron external effect parameter σ is in [-0.5,3]. Figure 7 The bifurcation diagram in (a) and Figure 7 The Lyapunov exponent spectrum in (b) shows that as the parameter σ continues to increase, the model remains in a hyperchaotic state, and the maximum Lyapunov exponent decreases as the parameter σ increases.

[0071] Figure 10 Shown are the phase diagrams of hyperchaotic attractors under different neuron external effect parameters σ: (a) σ = -0.8, (b) σ = 0.8, (c) σ = 2.8.

[0072] Figure 11 The figure shows the different neuron discharge patterns of the coupled neuron model when the parameters ε=-0.015, kr=-0.15, α=-0.015, β=-0.65, a=2.68, b=0.18, c=2.55, γ=3.8, μ=0.02, initial value φ0=(-1,-1,1,1,0), and parameter σ changes. When σ=-0.3, the coupled neuron model behaves as follows Figure 11 (a) shows the triangular cluster discharge mode, Figure 11 (b) shows the details of the triangular burst discharge. When σ = 0.85, the coupled neuron model is expressed as Figure 11 (c) shows the chaotic spike discharge mode I, Figure 11 (d) shows the details of chaotic spike discharge. When σ = 3, the coupled neuron model is expressed as Figure 11 (e) Chaotic spike discharge mode II, Figure 11 (d) shows the details of the chaotic spike discharge.

[0073] Figure 12 The figure shows other types of neuron firing patterns exhibited by the coupled neuron model when ε = -0.015, α = -0.015, β = -0.65, b = 0.18, c = 2.55, γ = 3.8, μ = 0.02, σ = 3, and initial value φ0 = (-1, -1, 1, 1, 0). When kr = -0.15a = 1.68, the model appears as Figure 12 (a) The resting state. When kr=-0.15a=1.68, the model presents Figure 12 (a) The resting state. When kr = 0, a = 0.68, the model presents Figure 12 (b) The spike discharge mode.

[0074] Figure 13The following are the three-dimensional spectral entropy (SE) complexity under different parameters and initial values: when ε = 0.1, α = -0.35, β = -0.65, a = 0.695, b = 0.18, γ = 3.8, u = 0.0, initial value φ0 = (-1, -1, 1, 1, 0), (a) σ∈[0, 2.5], kr∈[-0.1, -0.4], c = 1.75; (b) kr∈[-0.1, 0.4], c∈[-1, 2.5], σ = 1.5; when k = 1.5, kr = 0.4, c = 1.75, σ = 1.5, γ = 3.8, u = 0.01, initial value φ0 = (-1, -1, 1, 1, 0) When, (c) α∈[-0.5,0.5], β∈[-1,-0.4], a=0.695, b=0.18; (d) a∈[0,0.7], b∈[0,0.5], α=-0.35, β=-0.65; when k=0.1, α=-0.01, β=-0.65, a=0. 695, b=0.18, c=1,8, σ=1.75, γ=3.8, u=0.01, (e)kr∈[-0.1,0.1], y2(0)∈[-1,1.5]; (f)y1(0)∈[-0.5,0.5], y2(0)∈[-1,1.5], kr=0.03. Under these parameter conditions, the SE complexity of the model is very high and the chaotic sequence generated by the model is highly random.

[0075] The above analysis demonstrates that this novel discrete memristor coupled heterogeneous neuron model exhibits rich dynamical behavior, generating attractors of hyperchaotic, chaotic, and periodic states, as well as a variety of neuron discharge patterns, when its parameters are varied. Furthermore, its high complexity suggests that this coupled neuron model is suitable for applications such as image encryption.

[0076] S4. Implementation of a novel discrete memristor-coupled heterogeneous neuron model based on DSP.

[0077] The present invention realizes the memristor-coupled neuron model based on a 32-bit TMS320F2855 chip.

[0078] Figure 14 This is the hardware connection diagram of the TMS320F2855 chip, communication interface and DA converter when implementing DSP. Figure 15 Physical connection diagram for DSP implementation. Figure 16 This is the result diagram of DSP implementation.

[0079] Step 1: Connect the various hardware components. The TMS320F2855 chip is connected to the computer via the MAX3232 communication interface, and to the oscilloscope UTD7102 via the DAC8552 DA converter.

[0080] Step 2: Initialize the DSP chip on the CCS platform on the computer and configure the GPIO port.

[0081] Step 3: Set various parameters, initial values, and iteration steps to obtain a discrete coupled heterogeneous neuron model on the CCS platform. Since the digital quantity converted by the DA converter is a positive integer from 0 to 65535, the generated sequence needs to be translated and amplified.

[0082] Step 4: Load the corresponding program into the DSP chip. The chaotic sequences generated by the model will be transmitted to the oscilloscope through the DA converter, and the two-dimensional attractor will be displayed on the oscilloscope screen.

[0083] According to the above steps, set the parameters ε=0.1, β=-0.65, a=0.7, b=0.18, c=1.9, μ=0.01, and the initial value φ0=(-1,-1,1,0,0). After debugging, if Figure 16 As shown, the hyperchaotic attractor is displayed on the oscilloscope, which is consistent with the MATLAB simulation results. Figure 16 :(a) Hyperchaotic attractor I (kr=0.3,α=-0.35,γ=4.8,σ=1.35), (b) Hyperchaotic attractor II (kr=0.45,α=-0.25,γ=3.8,σ=1.8), (c) Hyperchaotic attractor I, (d) Hyperchaotic attractor II.

[0084] S5. Combine the chaotic sequence generated by the designed novel discrete memristor coupled heterogeneous neuron model with the scrambling and diffusion algorithms to perform image encryption and perform image encryption performance testing. Process the plaintext image I based on the model obtained in step S4;

[0085] Step 1: Input the plaintext image I and record the image height H and width W;

[0086] Step 2: Determine a set of parameters and initial values: ε = 3.8, kr = -0.1, α = -0.015, β = -0.65, a = 2.695, b = 0.18, γ = 4.8, μ = 0.02, σ = -0.2. When the initial value φ0 = (-1, -1, 0, 1, 1), iterate the model obtained in step S4 H × W times to obtain four sets of chaotic sequences. The formula is as follows:

[0087]

[0088] Where X, Y, Z, and U are the chaotic sequences of iterative operations of the neuron state variables x1, z, x2, and y2 in the coupled neuron model, floor represents the rounding down operation, and mod represents the modulo operation.

[0089] Step 3: The generated four chaotic sequences are used to scramble the plaintext image I, and the pixel position of the scrambled image I1 is obtained, and the formula is as follows:

[0090]

[0091] In the formula, i and j are the row and column pixel coordinates of the plaintext image, ii and jj are the row and column pixel coordinates of the scrambled image, (ii,jj) is the pixel position of the scrambled image, and double represents the conversion of floating-point type.

[0092] Step 4: The scrambled image I1 is converted into a vector, and a diffusion operation is performed to change the pixel value of the image, and the formula is as follows:

[0093]

[0094] In the formula, I1(i) is the pixel value of the scrambled image, and I2(i) is the pixel value of the image converted into a vector after the diffusion operation.

[0095] Step 5: The symmetric encryption algorithm is used to complete the decryption of the image.

[0096] Figure 17 The results of the encryption and decryption of the gray-scale images with a size of 512x512 and 256x256 using the chaotic sequence generated by the coupled neuron model and the simple encryption and decryption algorithm are shown in (a) plaintext image, (b) ciphertext image, and (c) decrypted image.

[0097] Figure 18 The performance test results of image encryption are shown in (a) pixel distribution histogram of the plaintext image, (b) pixel distribution histogram of the ciphertext image, (c) correlation of the plaintext image in the horizontal, vertical, and diagonal directions, and (d) correlation of the ciphertext image in the horizontal, vertical, and diagonal directions. The comparison results show that the new discrete memristive coupled heterogeneous neuron model has higher security when applied to image encryption.

[0098] The chaotic sequence generated by the coupled neuron model is an important part of image encryption. In the image scrambling stage, the pixel position is disturbed, and the chaotic sequence and the scrambling algorithm are combined to destroy the spatial correlation. In the image diffusion stage, the pixel value is changed, and the chaotic sequence and the diffusion algorithm are combined to destroy the statistical properties. The initial value sensitivity, pseudo-randomness, and ergodicity of the new discrete memristive coupled heterogeneous neuron model ensure the security of image encryption.

[0099] The above shows and describes the basic principles and main features of the present application and the advantages of the present application, and those skilled in the art should understand that the present application is not limited to the above embodiments, and the above embodiments and descriptions in the specification are only to illustrate the principles of the present application, and various changes and improvements can be made to the present application without departing from the spirit and scope of the present application, and these changes and improvements all fall within the scope of the claimed present application, and the scope of protection of the present application is defined by the appended claims and their equivalents.

Claims

1. A novel discrete memristor coupled heterogeneous neuron model construction and application, characterized by: include: Memristor building module, coupling module, dynamic analysis module, and DSP building module.

2. The novel discrete memristor coupled heterogeneous neuron model construction and application according to claim 1 is characterized in that: M1: The memristor building block is implemented as follows: Based on the definition of memristor, the mathematical model of discrete memristor is obtained as follows: Where u(n) is the input of the memristor, x(n) is the output of the memristor, z(n) represents the state variable of the memristor, h(·) represents the memristor form of the discrete memristor, and f(·) represents the intermediate state variable expression of the discrete memristor.

3. The novel discrete memristor coupled heterogeneous neuron model construction and application according to claim 1 is characterized in that: M2: The coupling module is implemented as follows: The discrete memristor obtained in step M1 is used to simulate synapses to couple two different discrete neuron models F1(·) and F2(·) to construct the final novel discrete memristor coupled heterogeneous neuron model. The formula is as follows: Where x1, y1, x2, y2 are neuron state variables, z is the intermediate state variable of discrete memristor, I ext1 and I ext2 is the external stimulus, h(z(n))(x1(n)-x2(n)) is the discrete memristive synaptic current.

4. The novel discrete memristor coupled heterogeneous neuron model construction and application according to claim 1 is characterized in that the M3: dynamic analysis module is implemented as follows: The dynamic characteristics of the new discrete memristor coupled heterogeneous neuron model are analyzed, and the influence of changes in parameters and initial values ​​on the dynamic behavior of the model state variables is studied. Smaller model parameters, that is, initial values ​​less than 5 and close to the origin, are selected to determine appropriate model parameters and initial values ​​for the DSP implementation of the model.

5. The novel discrete memristor coupled heterogeneous neuron model construction and application according to claim 1 is characterized in that: M4: DSP building blocks are implemented as follows: A novel discrete memristor-coupled heterogeneous neuron model is implemented based on DSP. The memristor-coupled neuron model is implemented based on the 32-bit TMS320F2855 chip. The TMS320F2855 chip is connected to a computer via the MAX3232 communication interface and to the UTD7102 oscilloscope via the DAC8552 DA converter. The TMS320F2855 chip is initialized on the CCS platform on the computer and the GPIO port is configured.

6. A novel discrete memristor coupled heterogeneous neuron model construction method, characterized by: include: S1: Process the plaintext image I based on the novel discrete memristor coupled heterogeneous neuron model obtained in step M4; S1-1: Input plaintext image I and record image height H and width W; S1-2: Determine a set of parameters and initial values ​​ε=3.8, kr=-0.1, α=-0.015, β=-0.65, a=2.695, b=0.18, γ=4.8, μ=0.02, σ=-0.

2. When the initial value φ0=(-1,-1,0,1,1), iterate the model obtained in step S4 H×W times to obtain four sets of chaotic sequences. The formula is as follows: Where X, Y, Z, and U are the chaotic sequences of iterative operations of the neuron state variables x1, z, x2, and y2 in the coupled neuron model, floor represents the rounding down operation, and mod represents the modulo operation. S1-3: Use the four sets of chaotic sequences generated to perform scrambling operations on the plaintext image I, disrupting the pixel positions to obtain the image I1 after pixel position transformation. The formula is as follows: Where i and j represent the row and column pixel coordinates of the plaintext image I, ii and jj represent the row and column pixel coordinates of the scrambled image I1, (ii, jj) is the image pixel position after the scrambling operation, and double represents the conversion of floating-point type; S1-4: Convert the scrambled image I1 into a vector and perform diffusion operation to change the image pixel value. The formula is as follows: Where I1(i) is the pixel value of the scrambled image, I2 is the encrypted image obtained, and I2(i) is the pixel value of the image after being converted into a vector and subjected to diffusion operation; S1-5: Using a symmetric encryption algorithm, the inverse operation of encryption is performed to decrypt the image. The decrypted image is obtained by performing the inverse diffusion of the formula in S1-4 on I2 and then performing the inverse scrambling of the formula in S1-3.

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