A secure communication method based on proportional time-delay inertial fuzzy CG neural network

Abstract

The present invention belongs to the field of new generation information technology, and specifically relates to a secure communication method based on proportional time-delay inertia fuzzy CG neural network, which establishes a drive system and a response system based on proportional time-delay inertia fuzzy CG neural network; sets a synchronization error, designs a finite time quantized synchronization controller, and the response system realizes finite time synchronization between the response system and the drive system under the action of the finite time quantized synchronization controller, thereby realizing secure communication. The present invention introduces proportional time lag and inertia terms into the fuzzy CG neural network, and designs a finite time quantized synchronization controller, which solves the problem of finite time synchronization based on proportional time-delay inertia fuzzy CG neural network, and the proposed secure communication method improves the complexity and security of secure communication.

Description

Technical Field

[0001] The present invention relates to the field of new generation information technology, and in particular to a secure communication method based on proportional time-delay inertial fuzzy CG neural network. Background Art

[0002] In the practical application of neural networks, in order to cope with the ever-changing real-world problems, neural networks need to present complex dynamic states, so it is necessary to use high-order differential equations to describe the neural network system. Since inertial neural networks are the expression of second-order differential equations, compared with first-order differential equations, they themselves will cause the system to produce complex dynamic behaviors, such as chaos and bifurcation, so they have potential application value in the field of new generation information technology. On the other hand, in practical applications, inertial neural networks will produce uncertainty, fuzziness and time delay, so fuzzy logic and proportional time delay play an important role in the dynamic analysis of neural networks.

[0003] There are a large number of synchronization phenomena in nature and many disciplines. Compared with the research on realizing the synchronization of neural networks in infinite time, realizing the synchronization of neural networks in a finite time has more far-reaching significance for the new generation of information technology.

[0004] Bandwidth constraints in network communication systems limit the transmission speed of information on communication channels. The introduction of quantitative control can reduce its impact on control performance, alleviate the transmission pressure of communication channels, and save economic costs. Summary of the invention

[0005] The purpose of the present invention is to provide a secure communication method based on a proportional time-delay inertial fuzzy CG neural network, which can realize limited time synchronization based on a proportional time-delay inertial fuzzy CG neural network and improve the security of secure communication.

[0006] To achieve the above object, the present invention provides the following technical solution, a secure communication method based on proportional time-delay inertial fuzzy CG neural network, comprising the following steps:

[0007] Step S1: Establishing a proportional time-delay inertial fuzzy CG neural network drive system and response system, specifically including the following steps:

[0008] Step S11: Establish a proportional time-delay inertial fuzzy CG neural network as follows:

[0009]

[0010]

[0011] Wherein, time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the inertial fuzzy CG neural network; x i (t) represents the state of the i-th neuron of the inertial fuzzy CG neural network at time t; α i represents the damping coefficient of the i-th neuron, α i Satisfy α i >0; p i (·) represents the magnification function, and there exists a positive constant p i and H i The amplification function p i (·) satisfies the inequality: 0<p i (χ)≤p i ,|p i (χ)-p i (ψ)|≤H i |χ-ψ|, where χ and ψ are arbitrary real numbers; β i (·) represents the behavior function, and there exists a positive constant J i The amplification function p i (·) and the behavior function β i (·) satisfies the inequality: χ≠ψ; a ij 、b ij and c ij represents the connection weight; d ij is the feedforward element; h ij and m ij is the minimum element of fuzzy feedback; k ij and n ij is the largest element of fuzzy feedback; T ij and S ij They represent the minimum fuzzy feedforward element and the maximum fuzzy feedforward element respectively; f j (x j (t)) represents the activation function of the jth neuron in the inertial fuzzy CG neural network without time delay, f j (x j (τ j t)) represents the activation function of the j-th neuron in the inertial fuzzy CG neural network containing proportional time lag, represents the activation function of the jth neuron of the inertial fuzzy CG neural network with neutral time lag, τ j Represents the proportional lag factor and satisfies 0<τ j ≤1, and τ j t=t-(1-τ j )t, where (1-τ j )t represents the information transmission delay of the jth neuron at time t; the above activation functions all satisfy the Lipschitz condition, that is, and |f x (·)|≤M j ,in and ω are any real numbers, L j is a positive constant, M j is a positive constant; ∧ and ∨ represent the "fuzzy AND" and "fuzzy OR" operators respectively, and for any real number and ω satisfy the following conditions:

[0012]

[0013] V j (t) represents the input of the jth neuron and satisfies in is a positive constant; I i (t) represents the bias of the i-th neuron and satisfies |I i (t)|≤I i , where I i is a positive constant;

[0014] Step S12: Establishing a proportional time-delay inertia fuzzy CG neural network drive system as follows:

[0015] The proportional time-delay inertia fuzzy CG neural network established in step S11 is subjected to variable substitution and order reduction processing to establish a proportional time-delay inertia fuzzy CG neural network driving system as follows:

[0016]

[0017] Among them, ε i is a constant, and

[0018] Step S13: According to the driving system established in step S12, a corresponding response system is established:

[0019]

[0020] Wherein, time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the inertial fuzzy CG neural network; y i (t) represents the state of the i-th neuron of the response system at time t; w i (t) represents the z in the response system corresponding to the z in the drive system i (t) parameter; f j (y j (t)) represents the activation function of the jth neuron in the response system without time delay, f j (y j (τ jt)) represents the activation function of the j-th neuron in the response system including proportional time lag, represents the activation function of the jth neuron in the response system with neutral time delay; the above activation functions all satisfy the Lipschitz condition, that is, in and ω are any real numbers, L j is a positive constant and satisfies |f j (·)|≤M j , where M j is a positive constant; and represents a finite-time quantized synchronous controller;

[0021] Step S2: according to the drive system and response system based on the proportional time-delay inertia fuzzy CG neural network established in step S1, setting the synchronization error;

[0022] Step S3: According to the synchronization error constructed in step S2, a finite-time quantized synchronization controller is designed, and the finite-time quantized synchronization controller is applied to the response system so that the response system is synchronized with the drive system, thereby realizing a confidential communication method.

[0023] Furthermore, step S2 is specifically as follows:

[0024] According to the drive system and response system based on the proportional time-delay inertia fuzzy CG neural network constructed in step S1, the synchronization error of the drive system and response system is set to:

[0025]

[0026] Furthermore, step S3 specifically includes the following contents:

[0027] Step S31: Design a finite time quantized synchronization controller according to the synchronization error constructed in step S2:

[0028]

[0029] Where i = 1, 2, ..., n; σ1, σ2, λ and θ are positive controller gains; 0 < η < 1; sign(·) is the sign function; g(e 1i (t)) is the error e 1i The quantized value of (t), g(e 1i (t))=(1+Δ)e 1i (t), Δ is the quantization error, is a sector boundary, 0<δ<1; g(e2i(t)) is the quantized value of the error e2i(t), where g(e2i(t))=(1+Δ)e 2i(t); the controller gains σ1, σ2 and θ satisfy the following inequalities:

[0030]

[0031]

[0032] Step S32: applying the finite time quantized synchronization controller to the response system, so that the response system is synchronized with the drive system;

[0033] Step S33: After the drive system is synchronized with the response system, the sending end obtains the chaotic signal generated by the drive system as the encrypted signal x i (t), the receiving end obtains the chaotic signal generated by the response system as the decryption signal y i (t);

[0034] Step S34: The transmitting end encrypts the signal x i (t) and the plaintext signal s i (t) Perform encryption operation to obtain the ciphertext signal h i (t), h i (t) = x i (t)+s i (t);

[0035] Step S35: The transmitting end sends the ciphertext signal h through the channel i (t), the receiving end receives the ciphertext signal h through the channel i (t);

[0036] Step S36: The receiving end receives the plaintext signal h i (t) and the decrypted signal y i (t) Perform decryption operation to obtain the decrypted plaintext signal ss i (t), ss i (t) = h i (t)-y i (t).

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. In the present invention, inertia terms and fuzzy operators are introduced into the CG neural network, which has more complex dynamic behavior than the first-order neural network, and increases the difficulty of cracking confidential communications.

[0039] 2. The present invention designs a finite time synchronous quantization controller. This type of synchronous convergence time can be optimized by adjusting the initial value, so that the neural network can achieve the desired synchronization characteristics in a controllable time and realize the reasonable optimization of resources. At the same time, after the quantizer is introduced into the control system, the burden of the communication channel and the impact of bandwidth constraints on system performance can be reduced, saving system resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of a secure communication method based on proportional time-delay inertial fuzzy CG neural network of the present invention;

[0041] Figure 2 The change trajectory diagram of the driving system and the response system without the action of the controller, where (a) is the trajectory diagram of x1(t) and y1(t) without the action of the controller; (b) is the trajectory diagram of x2(t) and y2(t) without the action of the controller; (c) is the trajectory diagram of z1(t) and w1(t) without the action of the controller; (d) is the trajectory diagram of z2(t) and w2(t) without the action of the controller;

[0042] Figure 3 is the synchronization error e without controller action 11 (t), e 12 (t), e 21 (t) and e 22 (t) change trajectory diagram;

[0043] Figure 4 The changing trajectory diagram of the driving system and the response system under the action of the finite time quantized synchronous controller, where (a) is the trajectory diagram of x1(t) and y1(t) under the action of the finite time quantized synchronous controller; (b) is the trajectory diagram of x2(t) and y2(t) under the action of the finite time quantized synchronous controller; (c) is the trajectory diagram of z1(t) and w1(t) under the action of the finite time quantized synchronous controller; (d) is the trajectory diagram of z2(t) and w2(t) under the action of the finite time quantized synchronous controller;

[0044] Figure 5 is the error trajectory diagram under the action of the finite time quantized synchronous controller, where (a) is the synchronization error e under the action of the finite time quantized synchronous controller 11 (t), e 12 (t), e 21 (t) and e 22 (t) is the changing trajectory of g(e) under the action of finite time quantized synchronous controller; (b) is the changing trajectory of g(e) under the action of finite time quantized synchronous controller 11 (t))、g(e 12 (t))、g(e 21 (t)) and g(e 22(t))’s changing trajectory. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] Embodiment 1:

[0047] like Figure 1 As shown, this embodiment provides a secure communication method based on a proportional time-delay inertial fuzzy CG neural network, the method comprising the following steps:

[0048] Step S1: Establishing a proportional time-delay inertial fuzzy CG neural network drive system and response system, specifically including the following steps:

[0049] Step S11: Establish a proportional time-delay inertial fuzzy CG neural network as follows:

[0050]

[0051] Wherein, time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the inertial fuzzy CG neural network; x i (t) represents the state of the i-th neuron of the inertial fuzzy CG neural network at time t; α i represents the damping coefficient of the i-th neuron, α i Satisfy α i >0; p i (·) represents the magnification function, and there exists a positive constant p i and H i The amplification function p i (·) satisfies the inequality: 0<p i (X)≤p i ,|p i (X)-p i (ψ)|≤H i |X-ψ|, where X and ψ are arbitrary real numbers; β i (·) represents the behavior function, and there exists a positive constant J i The amplification function p i (·) and the behavior function β i (·) satisfies the inequality: X≠ψ; a ij 、b ij and c ijrepresents the connection weight; d ij is the feedforward element; h ij and m ij is the minimum element of fuzzy feedback; k ij and n ij is the largest element of fuzzy feedback; T ij and S ij They represent the minimum fuzzy feedforward element and the maximum fuzzy feedforward element respectively; f j (x j (t)) represents the activation function of the jth neuron in the inertial fuzzy CG neural network without time delay, f j (x j (τ j t)) represents the activation function of the j-th neuron in the inertial fuzzy CG neural network containing proportional time lag, represents the activation function of the jth neuron of the inertial fuzzy CG neural network with neutral time lag, τ j Represents the proportional lag factor and satisfies 0<τ j ≤1, and τ j t=t-(1-τ j )t, where (1-τ j )t represents the information transmission delay of the jth neuron at time t; the above activation functions all satisfy the Lipschitz condition, that is, and |f j (·)|≤M j ,in and ω are any real numbers, L j is a positive constant, M j is a positive constant; ∧ and ∨ represent the "fuzzy AND" and "fuzzy OR" operators respectively, and for any real number and ω satisfy the following conditions:

[0052]

[0053] V j (t) represents the input of the jth neuron and satisfies in is a positive constant; I i (t) represents the bias of the i-th neuron and satisfies |I i (t)|≤I i , where I i is a positive constant;

[0054] Step S12: Establishing a proportional time-delay inertia fuzzy CG neural network drive system as follows:

[0055] The proportional time-delay inertia fuzzy CG neural network established in step S11 is subjected to variable substitution and order reduction processing to establish a proportional time-delay inertia fuzzy CG neural network driving system as follows:

[0056]

[0057] Among them, ε i is a constant, and

[0058] Step S13: According to the driving system established in step S12, a corresponding response system is established:

[0059]

[0060] Wherein, time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the inertial fuzzy CG neural network; y i (t) represents the state of the i-th neuron of the response system at time t; w i (t) represents the z in the response system corresponding to the z in the drive system i (t) parameter; f j (y j (t)) represents the activation function of the jth neuron in the response system without time delay, f j (y j (τ j t)) represents the activation function of the j-th neuron in the response system including proportional time lag, represents the activation function of the jth neuron in the response system with neutral time delay; the above activation functions all satisfy the Lipschitz condition, that is, in and ω are any real numbers, L j is a positive constant and satisfies |f j (·)|≤M j , where M j is a positive constant; and represents a finite-time quantized synchronous controller;

[0061] Step S2: according to the drive system and response system based on the proportional time-delay inertia fuzzy CG neural network established in step S1, setting the synchronization error;

[0062] Step S3: According to the synchronization error constructed in step S2, a finite-time quantized synchronization controller is designed, and the finite-time quantized synchronization controller is applied to the response system so that the response system is synchronized with the drive system, thereby realizing a confidential communication method.

[0063] In this embodiment, step S2 includes the following steps:

[0064] According to the drive system and response system based on the proportional time-delay inertia fuzzy CG neural network constructed in step S1, the synchronization error of the drive system and response system is set to:

[0065]

[0066] In this embodiment, step S3 includes the following steps:

[0067] Step S31: Design a finite time quantized synchronization controller according to the synchronization error constructed in step S2:

[0068]

[0069] Where i = 1, 2, ..., n; σ1, σ2, λ and θ are positive controller gains; 0 < η < 1; sign(·) is the sign function; g(e 1i (t)) is the error e 1i The quantized value of (t), g(e 1i (t))=(1+Δ)e 1i (t), Δ is the quantization error, is a sector boundary, 0<δ<1; g(e2i(t)) is the quantized value of the error e2i(t), where g(e2i(t))=(1+Δ)e 2i (t); the controller gains σ1, σ2 and θ satisfy the following inequalities:

[0070]

[0071] Step S32: applying the finite time quantized synchronization controller to the response system, so that the response system is synchronized with the drive system;

[0072] Step S33: After the drive system is synchronized with the response system, the sending end obtains the chaotic signal generated by the drive system as the encrypted signal x i (t), the receiving end obtains the chaotic signal generated by the response system as the decryption signal y i (t);

[0073] Step S34: The transmitting end encrypts the signal x i (t) and the plaintext signal s i (t) Perform encryption operation to obtain the ciphertext signal h i (t), h i (t) = x i (t)+s i (t);

[0074] Step S35: The transmitting end sends the ciphertext signal h through the channel i (t), the receiving end receives the ciphertext signal h through the channel i (t);

[0075] Step S36: The receiving end receives the plaintext signal h i (t) and the decrypted signal y i (t) Perform decryption operation to obtain the decrypted plaintext signal ss i (t), ss i (t) = h i (t)-y i (t).

[0076] It is worth noting that, in the present invention, the inertia term and fuzzy operator are introduced into the CG neural network, which has more complex dynamic behavior than the first-order neural network, and increases the difficulty of cracking the confidential communication. In the present invention, a finite-time synchronous quantization controller is designed. This type of synchronous convergence time can be optimized by adjusting the initial value, so that the neural network can achieve the desired synchronization characteristics within a controllable time, and realize the reasonable optimization of resources. At the same time, after the quantizer is introduced into the control system, the burden of the communication channel and the influence of the bandwidth constraint on the system performance can be reduced, saving system resources.

[0077] Embodiment 2:

[0078] This embodiment mainly includes two parts:

[0079] One is to theoretically prove the effectiveness of the secure communication method based on proportional time-delay inertial fuzzy CG neural network proposed in Example 1.

[0080] Secondly, the synchronization performance of the inertial fuzzy CG neural network drive system and response system with proportional time lag in Example 1 is verified by numerical simulation.

[0081] (Theoretical proof and simulation experiment are not used to limit the present invention. In other embodiments, simulation experiment may not be performed, and other experimental schemes may be used to test and verify the performance of the neural network system.)

[0082] 1. Theoretical Proof

[0083] Define the synchronization error between the drive system and the response system: e 1i (t) = y i (t)-x i (t), e 2i (t) = w i (t)-z i(t), the synchronous error system can be obtained from the driving system and the response system as follows

[0084]

[0085] The following are the definitions and lemmas that will be used in the proof:

[0086] Definition 1: For T>0 that depends on the initial value, if for all t≥T, there is And|y i (t)-x i (t)|=0,|w i (t)-z i (t)|=0, then the driving system and the response system are said to achieve finite-time synchronization within T;

[0087] Lemma 1: Assume there exists a regular, positive definite and radially unbounded function V(t): R n →R + ∪{0}, so that any solution of the error system satisfies the inequality:

[0088]

[0089] Where γ>0, 0<Γ<1, and V(t) satisfies: V 1 - Γ (t)≤V 1-Γ (0)-γ(1-Γ)(t-0), 0≤t≤T; V(t)=0, Then the upper bound of time T is expressed by the following formula:

[0090]

[0091] Lemma 2: Assume u1,u2,...,u n ≥0, 0<p≤1, q>1, then

[0092]

[0093] Next, construct the Lyapunov functional:

[0094]

[0095] Then, the derivative of the constructed Lyapunov functional is calculated:

[0096]

[0097]

[0098]

[0099] According to the bounded activation function, the following inequality can be obtained:

[0100]

[0101]

[0102] And according to the amplification function p i (·), behavior function β i (·) and neuron j input V j (t) is defined, then We can further get:

[0103]

[0104]

[0105] And because the parameters σ1, σ2 and θ satisfy the following inequalities:

[0106]

[0107] Then it can be deduced that:

[0108]

[0109] According to Lemma 3, we can get:

[0110]

[0111] Based on Lemma 1, we can get 2λ(1+δ) η >0; T is as follows:

[0112]

[0113] Therefore, according to Definition 1 and Lemma 1, It can be seen that under the action of the finite-time quantized synchronization controller, the drive system and the response system achieve finite-time synchronization within T.

[0114] 2. Numerical Simulation

[0115] In this embodiment, taking a proportional time-delay inertia fuzzy CG neural network containing two neurons as an example, the driving system and the response system are determined as follows:

[0116]

[0117] The specific parameters are as follows: i = 1, 2; j = 1, 2; t ≥ 0; proportional lag is τ j t=t-(1-τ j)t,τ1=τ2=0.7;f1(x1(t))=tanh(x1(t));f2(x2(t))=tanh(x2(t));f1(x1(τ1t))=tanh(x1(t-(1-τ1)t));f2(x2(τ2t))=tanh(x2(t-(1-τ2)t)); f1(y1(t))=tanh(y1(t));f2(y2(t))=tanh(y2(t));f1(y1(τ1t))=tanh(y1(t-(1-τ1)t));f2(y2(τ2t))=tanh(y2(t-(1-τ2)t)); β1(x1(t))=0.4x1(t);β2(x2(t))=0.4x2(t);β1(y1(t))=0.4y1(t);β2(y2(t))=0.4y2(t);ε1=ε2=3;α1=α2=9;a 11 =0.3、a 12 =0.1、a 21 =-0.1、a 22 =0.2;b 11 =-0.4、b 12 =0.2、b 21 =0.3、b 22 =0.1;c 11 =1、c 12 =1.5、c 21 =-1、c 22 =2;d 11 =0.4、d 12 =0.2、d 21 =0.25、d 22 =0.3;T 11 =1、T 12 =-1、T 21 =-0.9、T 22 =1;S 11 =-1、S 12 =1、S 21 =0.9、S 22 =-1;h 11 =-0.6、h 12 =0.5、h 21 =-0.4、h 22 =0.8;k 11 =-1、k 12 =2、k 21 =-2、k 22 =1.8;m 11 =2、m 12=-1.5, m 21 =1.4, m 22 =-1.8; n 11 =2.6, n 12 =-3.5, n 21 =2.6, n 22 =-2.8; external input V1(t) = 1, V2(t) = 1, take I1(t)=4cos(t), 12(t)=4sin(t), take I i =4; let M j =1, J i =0.12, H i =0.05; p i =0.4, δ=0.25;

[0118] According to the above parameter settings and inequality:

[0119]

[0120]

[0121] The parameter value ranges are: σ1≥5.668, σ2≥3.268, θ≥6.92; according to the requirements of the finite-time quantized synchronous controller λ>0, 0<η<1; take σ1=5.7, σ2=3.3, θ=7, λ=1, η=0.5; according to Lemma 1, we can get T=3.476.

[0122] The drive system, response system and finite time quantized synchronous controller are numerically simulated under the above parameters. The initial values ​​of the drive system and response system are set as follows: x1(0)=1, x2(0)=1, z1(0)=1, z2(0)=1, y1(0)=-1, y2(0)=-0.5, w1(0)=-1, w2(0)=-1, t>0.

[0123] The specific simulation experiment results are as follows: Figure 2 The change trajectory diagram of the driving system and the response system without the action of the controller, where (a) is the trajectory diagram of x1(t) and y1(t) without the action of the controller; (b) is the trajectory diagram of x2(t) and y2(t) without the action of the controller; (c) is the trajectory diagram of z1(t) and w1(t) without the action of the controller; (d) is the trajectory diagram of z2(t) and w2(t) without the action of the controller; Figure 3 is the synchronization error e without controller action 11 (t), e 12 (t), e 21 (t) and e 22 (t) change trajectory diagram; Figure 4The changing trajectory diagram of the driving system and the response system under the action of the finite time quantized synchronous controller, where (a) is the trajectory diagram of x1(t) and y1(t) under the action of the finite time quantized synchronous controller; (b) is the trajectory diagram of x2(t) and y2(t) under the action of the finite time quantized synchronous controller; (c) is the trajectory diagram of z1(t) and w1(t) under the action of the finite time quantized synchronous controller; (d) is the trajectory diagram of z2(t) and w2(t) under the action of the finite time quantized synchronous controller; Figure 5 is the error trajectory diagram under the action of the finite time quantized synchronous controller, where (a) is the synchronization error e under the action of the finite time quantized synchronous controller 11 (t), e 12 (t), e 21 (t) and e 22 (t) is the changing trajectory of g(e) under the action of finite time quantized synchronous controller; (b) is the changing trajectory of g(e) under the action of finite time quantized synchronous controller 11 (t))、g(e 12 (t))、g(e 21 (t)) and g(e 22 (t)) change trajectory diagram. Among them, Figure 2 and Figure 3 It shows that the drive system and the response system cannot be synchronized without the action of the controller; Figure 4 and Figure 5 It shows that under the action of the finite-time quantized synchronization controller, the response system is synchronized with the drive system, verifying the synchronization performance.

[0124] Finally, it should be noted that the above description is only a preferred example of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A secure communication method based on proportional time-delay inertial fuzzy CG neural network, characterized in that: The following steps are involved: Step S1: Establishing a proportional time-delay inertial fuzzy CG neural network drive system and response system, specifically including the following steps: Step S11: Establish a proportional time-delay inertial fuzzy CG neural network as follows: Wherein, time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the inertial fuzzy CG neural network; x i (t) represents the state of the i-th neuron of the inertial fuzzy CG neural network at time t; α i represents the damping coefficient of the i-th neuron, α i Satisfy α i >0;p i (·) represents the magnification function, and there exists a positive constant p i and H i The amplification function p i (·) satisfies the inequality: 0 <p i (χ)≤p i ,|p i (χ)-p i (ψ)|≤H i |χ-ψ|, where χ and ψ are arbitrary real numbers; β i (·) represents the behavior function, and there exists a positive constant J i The amplification function p i (·) and the behavior function β i (·) satisfies the inequality: a ij , b ij and c ij represents the connection weight; d ij is the feedforward element; h ij and m ij is the minimum element of fuzzy feedback; k ij and n ij is the largest element of fuzzy feedback; T ij and S ij They represent the minimum fuzzy feedforward element and the maximum fuzzy feedforward element respectively; f j (x j (t)) represents the activation function of the jth neuron in the inertial fuzzy CG neural network without time delay, f j (x j (τ j t)) represents the activation function of the j-th neuron in the inertial fuzzy CG neural network containing proportional time lag, represents the activation function of the jth neuron of the inertial fuzzy CG neural network with neutral time lag, τ j represents the proportional lag factor and satisfies 0<τ j ≤1, and τ j t=t-(1-τ j )t, where (1-τ j )t represents the information transmission delay of the jth neuron at time t; the above activation functions all satisfy the Lipschitz condition, that is, and |f j (·)|≤M j ,in and ω are any real numbers, L j is a positive constant, M j is a positive constant; ∧ and ∨ represent the "fuzzy AND" and "fuzzy OR" operators respectively, and for any real number and ω satisfy the following conditions: V j (t) represents the input of the jth neuron and satisfies in is a positive constant; I i (t) represents the bias of the i-th neuron and satisfies |I i (t)|≤I i , where I i is a positive constant; Step S12: Establishing a proportional time-delay inertia fuzzy CG neural network driving system; The proportional time-delay inertia fuzzy CG neural network established in step S11 is subjected to variable substitution and order reduction processing to establish a proportional time-delay inertia fuzzy CG neural network driving system as follows: Among them, ε i is a constant, and Step S13: According to the driving system established in step S12, a corresponding response system is established: Wherein, time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the inertial fuzzy CG neural network; y i (t) represents the state of the i-th neuron of the response system at time t; w i (t) represents the z in the response system corresponding to the z in the drive system i (t) parameter; f j (y j (t)) represents the activation function of the jth neuron in the response system without time delay, f j (y j (τ j t)) represents the activation function of the j-th neuron in the response system including proportional time lag, represents the activation function of the jth neuron in the response system with neutral time delay; the above activation functions all satisfy the Lipschitz condition, that is, and |f j (·)|≤M j ,in and ω are any real numbers, L j is a positive constant, M j is a positive constant; and represents a finite-time quantized synchronous controller; Step S2: according to the drive system and response system based on the proportional time-delay inertia fuzzy CG neural network established in step S1, setting the synchronization error; Step S3: designing a finite time quantized synchronization controller according to the synchronization error constructed in step S2, and applying the finite time quantized synchronization controller to the response system so that the response system is synchronized with the drive system, thereby realizing a confidential communication method; Step S3 specifically includes the following steps: Step S31: Design a finite time quantized synchronization controller according to the synchronization error constructed in step S2: where σ1, σ2, λ, and θ are positive controller gains; 0<η<1; sign(·) is the sign function; g(e 1i (t)) is the error e 1i The quantized value of (t), g(e 1i (t))=(1+Δ)e 1i (t), Δ is the quantization error, is a sector boundary, 0<δ<1; g(e 2i (t)) is the error e 2i (t), where g(e 2i (t))=(1+Δ)e 2i (t); the controller gains σ1, σ2 and θ satisfy the following inequalities: Step S32: applying the finite time quantized synchronization controller to the response system, so that the response system is synchronized with the drive system; Step S33: After the drive system is synchronized with the response system, the sending end obtains the chaotic signal generated by the drive system as the encrypted signal x i (t), the receiving end obtains the chaotic signal generated by the response system as the decryption signal y i (t); Step S34: The transmitting end encrypts the signal x i (t) and the plaintext signal s i (t) Perform encryption operation to obtain the ciphertext signal h i (t), h i (t) = x i (t)+s i (t); Step S35: The transmitting end sends the ciphertext signal h through the channel i (t), the receiving end receives the ciphertext signal h through the channel i (t); Step S36: The receiving end receives the plaintext signal h i (t) and the decrypted signal y i (t) Perform decryption operation to obtain the decrypted plaintext signal ss i (t), ss i (t) = h i (t)-y i (t).

2. The secure communication method based on proportional time-delay inertial fuzzy CG neural network according to claim 1 is characterized in that: Step S2 is specifically as follows: According to the drive system and response system based on the proportional time-delay inertia fuzzy CG neural network constructed in step S1, the synchronization error of the drive system and response system is set to:

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