A Secure Binary Synchronization Method Based on Average Quasi-Periodic Intermittent Control of Coupled Neural Networks

Abstract

This invention discloses a secure binary synchronization method for coupled neural networks based on average quasi-periodic intermittent control. By constructing a coupled neural network model comprising a target network and multiple follower networks, an error model between the follower and target networks is defined. Deception attack and random disturbance models are established for the intermittent control and non-control intervals, respectively. Using hybrid system theory, stochastic Lyapunov stability theory, and matrix inequality techniques, sufficient conditions for ensuring the mean-square exponential stability of the error system are derived. An aperiodic intermittent security controller is designed, which, by adjusting the control gain parameter and control interval, ensures the mean-square bounded stability of the error system, achieving secure binary synchronization of the coupled neural network. This method improves the control resilience and adaptability of the network under attacks and disturbances, and is applicable to distributed collaborative and secure control scenarios such as smart grids and sensor networks.

Description

Technical Field

[0001] This invention relates to a secure binary synchronization method for coupled neural networks based on average quasi-periodic intermittent control, belonging to the field of network security and control technology. Background Technology

[0002] Neural networks are widely used to simulate complex dynamic systems, and they have important applications in optimization computation, image recognition, and artificial intelligence. Neural networks often exhibit rich chaotic dynamics; for example, various chaotic modes have been observed in low-dimensional autonomous structures. Research shows that the realization of associative memory in the mammalian brain is closely related to chaotic attractors and neuronal synchronization. Synchronization, as a typical collective behavior, is widely present in structures such as neural circuits and is one of the core phenomena of neural network dynamics. Early research focused on the synchronization behavior of simple master-slave chaotic systems and ideal systems such as the Kuramoto model. In recent years, the synchronization problem of large-scale coupled nonlinear networks has gradually become a core challenge and cutting-edge topic in this field, and a series of advances have been made. It is worth emphasizing that most existing synchronization control results for complex neural networks are based on the ideal assumption of fully cooperative connections between nodes, i.e., considering only unsigned coupled topologies with non-negative connection weights.

[0003] However, in practical applications, cooperative and competitive relationships often coexist among nodes. For example, interactions in social networks often include adversarial connections. Such systems are typically modeled using symbolic graphs, allowing negative edge weights, where positive weights represent friendly or cooperative relationships, and negative weights correspond to competitive or adversarial relationships. In such symbolically coupled networks, synchronization behavior exhibits a unique clustering phenomenon, namely binary synchronization: some nodes converge to a certain manifold, while the remaining nodes synchronize to their opposite state. In the past decade, the binary synchronization (or binary consistency) problem has attracted extensive research and made significant progress. However, most of these studies are based on an ideal assumption that the network coupling or control process is not subject to any malicious network attacks or external interference.

[0004] While networking technologies enhance the scalability and flexibility of complex networks, they also significantly increase the security threats faced by these systems. Malicious attackers can launch attacks against sensing, control, and execution units through open networks, especially threatening scale-free networks that are robust to random failures but extremely vulnerable to targeted attacks, severely impacting system reliability. Against this backdrop, achieving secure collaborative control of complex networks under malicious attack environments and ensuring the reliable achievement of their collective behaviors (such as synchronization) has become a key issue of common concern in industry and academia. Network security control needs to guarantee the confidentiality, availability, and integrity of information, mainly facing two types of attacks: denial-of-service attacks, which disrupt system availability by interrupting communication or introducing delays; and spoofing attacks, which compromise data integrity by tampering with communication signals. These attacks are highly covert and difficult to detect, thus attracting widespread attention from researchers. Existing anti-attack control research largely focuses on continuous control frameworks. Although secure synchronization strategies based on impulse control have emerged, research on attacks under discontinuous control frameworks such as aperiodic intermittent control remains relatively insufficient and urgently needs further exploration.

[0005] Based on the fact that intermittent communication can effectively simulate the impact of denial-of-service attacks on systems, intermittent control strategies, through alternating start-stop control operations, exhibit good engineering applicability and flexibility, and have been applied in systems such as multi-regional population diffusion. Due to external interference, equipment limitations, and sensing range constraints, real-world systems often cannot continuously implement control, making intermittent control more practically reasonable. Early research mainly focused on periodic intermittent control strategies, such as periodic control schemes in chaotic system synchronization; however, aperiodic intermittent control is more common in practical applications. Although various intermittent control methods have been proposed in recent years for achieving synchronization of nonlinear systems, most have not considered attack scenarios. Especially when attackers launch deception attacks targeting the controller or the controller-to-actuator channel, traditional methods are difficult to apply directly to secure synchronization control, mainly due to the following bottlenecks: First, under heterogeneous composite interference where the control section is subjected to deception attacks and the non-control section is subjected to random disturbances, the stability analysis methods of traditional periodic intermittent control are difficult to apply; second, when deception attacks and random disturbances act on the control and non-control parts respectively, forming hybrid dynamics, existing stability theories are unable to handle such mode-dependent heterogeneous interferences; furthermore, using upper and lower bound methods to characterize the frequency of aperiodic signals cannot reflect the actual statistical characteristics, resulting in conservative control protocols and limited performance. Therefore, designing an aperiodic intermittent control protocol that can resist deception attacks and random disturbances, enabling dynamic networks to achieve binary secure synchronization even under attack environments, has become a critical problem that urgently needs to be solved. Summary of the Invention

[0006] This invention provides a secure binary synchronization method for coupled neural networks based on average quasi-periodic intermittent control to address the problems existing in the prior art. This invention not only achieves mean-square bounded binary secure synchronization of coupled neural networks, but also enhances the control elasticity and adaptability of the system under attacks and disturbances.

[0007] The technical solutions adopted in this invention are as follows:

[0008] S1. Establish a complex coupled neural network control model with cooperative and adversarial links, specifically as follows:

[0009] consider Mean-square bounded safe binary synchronization control of a neural network, including the first... There are one follower network and one synchronous target network. The dynamic model of each follower network is given by the following equation:

[0010] (1);

[0011] in, , Indicates the first Each node dimensional state column vector; matrix Represents a diagonal matrix. Represents the weight matrix, and has Dimension; constant This represents the coupling strength.

[0012] Represents a nonlinear odd function. Represents the transpose of a vector; Indicates about The sign function; t is the time variable; control input The aim is to enable secure synchronization of coupled neural network models.

[0013] This invention is aimed at Each network defines a directed or undirected graph. ,in This represents a set containing N nodes. Denotes the edge set, while This represents a symbolically weighted adjacency matrix, whose elements are... .

[0014] For any ,like This indicates that from node To the node There exists a directed edge (when node) With nodes When indicating a cooperative relationship In a competitive relationship ); when node To the node When there are no connecting edges between them .

[0015] Laplace matrix Defined as ,in:

[0016] It is a degree matrix, and its diagonal elements Indicate the degree of node i;

[0017] , , represents the coupling effect from node j to node i, with the sign opposite to that of the adjacency matrix;

[0018] , , representing the total coupling input strength of node i.

[0019] The mathematical model of the target network presented in this invention is as follows:

[0020] (2);

[0021] in, This represents the state vector of the target network.

[0022] S2. Define the synchronization error variable between the follower network and the target network, and establish an error system model to describe the dynamic evolution of the error between the follower network and the target network, specifically:

[0023] First, the state of the follower network (i.e., Equation 1) is changed.

[0024] make , Combining the properties of the sign function and the Laplace matrix Definition and Since it is an odd function, formula (1) can be rearranged into the following form:

[0025] (3);

[0026] in: It represents the first derivative of the state vector of the i-th node of the following network with respect to time t after sign transformation;

[0027] Let represent a vector function consisting of m nonlinear odd functions, i=1,…,m.

[0028] This invention defines the first The binary synchronization state error variable of the follower network relative to the target network is: ,Right now Further transform the error state as follows: .

[0029] because ,when At that time, proof The state of the following network approaches the state of the target network. and Approaching They are equivalent.

[0030] Therefore, from formulas (1) and (3), we can obtain the first... The binary synchronization state error system model of the follower network relative to the target neural network is as follows:

[0031] (4);

[0032] in, Represents the error vector The first derivative with respect to time t;

[0033] , which is the nonlinear vector function of the error system model.

[0034] S3. For systems based on intermittent control, a hybrid threat modeling method between zones is adopted: a deception attack model is introduced in the control zone, and the success or failure of the attack is characterized by a Bernoulli random distribution; in the non-control zone, a random disturbance model is established, and the characteristics of the disturbance signal are described by a random process with specific statistical properties.

[0035] This invention provides a mathematical model for spoofing attacks and random disturbances in aperiodic intermittent controllers and the controller-actuator channel, including intermittent control intervals and non-control intervals. Spoofing attacks occur in the intermittent control intervals, while random disturbances occur in the intermittent control-non-control intervals. The probability of attacks and disturbances occurring is described using specific probability distributions.

[0036] Specifically, the replacement deception attack signal is represented as Introduce Bernoulli distribution variables related to the coupled neural network model. To describe the probability of a successful attack, let's assume a random variable. Independent of each other Represents a positive integer, and

[0037] (5);

[0038] in It is a constant. Represents a random variable at time t. The probability of taking the value 1 is equal to a constant. , Represents a random variable at time t. The probability of taking the value 0 is equal to a constant. .remember ,make for The expectation, that is .

[0039] In the intermittent control non-control interval, the random disturbance signal is represented as: The probability of a disturbance occurring is determined by a random variable. To describe, Indicates disturbance signal The probability of it occurring Among them, β i (t)=1 indicates the presence of a disturbance, β i (t)=0 indicates no disturbance.

[0040] S4. Based on hybrid system theory (used to characterize the switching behavior of a system under intermittent control), stochastic Lyapunov stability theory (used to handle the stability of stochastic differential systems with Bernoulli distribution variables), and matrix inequality techniques (used to transform stability conditions into solvable linear matrix inequality forms), this paper conducts an in-depth analysis of the mean-square boundedness of the dynamic system of synchronization error induced by a target network subjected to deception attacks and random disturbances. Finally, sufficient conditions that can ensure the mean-square exponential stability of this binary synchronization error system are derived.

[0041] S5. Design an aperiodic intermittent security controller suitable for deception attacks and random disturbance environments to achieve secure synchronization control of coupled neural networks. By reasonably configuring the gain parameters and intermittent control range of the controller, the mean square bounded stability of the synchronization error system is guaranteed, thereby achieving mean square bounded binary synchronization of coupled neural networks under the presence of attacks and interference.

[0042] During non-periodic transmission from the controller to the actuator, data packets are susceptible to spoofing attacks. If the attack succeeds, the actuator will receive maliciously modified false data instead of genuine control signals. In this scenario, the attacked control input can be described as follows:

[0043] (6);

[0044] The non-periodic intermittent controller is designed as follows:

[0045] (7);

[0046] in This is an adjustable gain parameter; and They represent the first Controlled and uncontrolled intervals It is the first One non-periodic intermittent control cycle; It is the first The first neural network of the nth neural network One intermittent control width; Indicates the first The first neural network of the nth neural network One uncontrolled width.

[0047] Combined with step S3, control the input. Further modeling is performed under deception attacks and random perturbations, specifically as follows:

[0048] (8);

[0049] Based on formula (4) in S2 and the definitions of deception attack and random perturbation in S3, the error system model formed by the follower network and the target network is further transformed (i.e., formula 4):

[0050] (9).

[0051] In S4 of this invention, an aperiodic intermittent control mechanism is designed to address the effects of deception attacks and disturbances. A Lyapunov function form is established in the stability analysis of the synchronization error system.

[0052] (10);

[0053] in Indicates the weighting factor. It is a symmetric positive definite metric matrix used to define the quadratic norm of the error system model.

[0054] Based on this, we obtain the sufficient condition for the mean-square bounded bipartite stability of the synchronization error system model (i.e., Equation 9):

[0055] (11);

[0056] (12);

[0057] (13);

[0058] in, , Representation matrix The minimum value of the real part of the eigenvalues, matrix , , , , , Represents the Laplace matrix, Represents the control gain matrix. Represents the control gain matrix The largest eigenvalue, Represents positive integers; , , , Represents a positive definite diagonal matrix. This represents the largest eigenvalue of the F matrix. Represents positive integers; Indicates the average intermittent control width. This indicates the average intermittent uncontrolled width.

[0059] Thus, by using matrix theory, we obtain linear matrix inequality conditions that are easy to solve with MATLAB, and determine the control gain that ensures the stability of the error system. Based on the above stability conditions, the control parameters in the aperiodic intermittent controller (i.e., Equation 7) are constructed, and the safe mean-square bounded synchronization problem between the dynamic model of the following network (i.e., Equation 1) and the target network (i.e., Equation 2) is equivalently transformed into a safe bounded stability problem of the error system. The control objective is to design a safe and attack-resistant aperiodic intermittent controller for each following network, i.e., to design the control gain in the controller (i.e., Equation 7) such that the tracking error system formed by it and the target network is mean-square eventually bounded, meaning the expected value of the system state converges to a compact set. ,Right now

[0060] (14);

[0061] in It is a positive number. This indicates that the expected state of the error system model (i.e., Equation 9) is less than or equal to .

[0062] Based on the above non-periodic intermittent security control method, the synchronization error system model under the influence of deception attack and disturbance (i.e., Equation 9) achieves mean square bounded stability, that is, the dynamic model of the following network (i.e., Equation 1) and the target network (i.e., Equation 2) finally achieve secure mean square binary synchronization control.

[0063] Traditional methods for secure synchronization control of complex coupled neural networks often employ periodic intermittent control strategies, which have inherent limitations such as low control resource utilization and limited ability to cope with complex network attacks. Especially when facing combined threats of coordinated deception attacks and random noise disturbances, traditional periodic intermittent control mechanisms struggle to achieve an effective balance between control efficiency, resource conservation, and system security robustness.

[0064] This invention constructs a complex coupled neural network attack model within an aperiodic intermittent control framework. This model simultaneously considers deception attacks initiated from the controller-actuator channel (i.e., attackers can inject forged data to replace real control commands) and ubiquitous random disturbances. For this model, this invention designs an aperiodic intermittent control strategy. By introducing the concepts of average control width and average non-control width, the macroscopic statistical characteristics of the aperiodic control / sleep interval sequence are used as the basis for stability analysis. This method greatly enhances the flexibility of intermittent control timing requirements, relaxes the strict constraints on the upper and lower bounds of each control interval duration, and makes controller design easier to implement in engineering. Based on hybrid control theory and Lyapunov stability theory, sufficient conditions are derived to ensure that the attacked coupled neural network achieves bipartite mean-square bounded synchronization. By co-designing coupling strength, attack probability, and average aperiodic intermittent control width, the desired upper bound of synchronization error is systematically adjusted and ultimately achieved. This means that developers can quantitatively calculate the required control resources or evaluate the degradation of synchronization performance under existing network conditions according to the different security and accuracy requirements of specific applications. The secure synchronization control method proposed in this invention is applied to scenarios requiring distributed coordination and security, such as the coordination of distributed generation units in smart grids and the security state estimation of sensor networks. The resulting benefits are:

[0065] 1) In response to the complex environment where deception attacks and random disturbances coexist, the concepts of average intermittent control interval and average non-control interval are proposed, which effectively solves the problem that traditional methods are difficult to accurately estimate the time statistical characteristics of non-periodic control signals, and provides a new approach for quantitative analysis of the frequency and duration of intermittent control.

[0066] 2) By introducing average control width and average non-control width, the traditional framework of relying on fixed upper and lower bound constraints / intermittent intervals is broken through, which significantly enhances the adaptability to non-periodic control sequences, reduces the conservatism of control design, and improves the practicality and flexibility of the method.

[0067] 3) By constructing an attack signal model with symbolic characteristics and using random variables to characterize the attack intensity, combined with the proposed average interval method, sufficient conditions are established to ensure that the coupled neural network achieves binary mean square bounded synchronization. The quantitative relationship between the synchronization error bound and the control parameters and attack intensity is clearly given, providing a theoretical basis and design criteria for the safe synchronization of the system. Attached Figure Description

[0068] Figure 1 A schematic diagram of a non-periodic intermittent control method for coupled neural networks to resist deception attacks and disturbances.

[0069] Figure 2 Target network chaotic attractor.

[0070] Figure 3 This is a directed topology graph of a complex coupled neural network.

[0071] Figure 4 This is a state binary synchronization trajectory diagram of the follower network and the target network under the control of this invention.

[0072] Figure 5 This refers to the error state between the follower network and the target network under the control of this invention. The change curve. Detailed Implementation

[0073] The invention will now be further described with reference to the accompanying drawings.

[0074] This embodiment proposes a secure binary synchronization method based on average quasi-periodic intermittent control of coupled neural networks (e.g., Figure 1 This method can effectively suppress the effects of deception attacks and random perturbations. The method is implemented according to the following steps:

[0075] S1: Construct a dynamic model of a complex coupled neural network under attack and disturbance conditions.

[0076] In this embodiment, the aim is to achieve mean-square-safe bounded synchronization control of a class of complex coupled neural networks. The system consists of one target network and five follower networks. The dynamic model of the i-th follower network is described as follows:

[0077] (15);

[0078] in, Indicates the first A state that follows the network; Indicates the internal coupling strength;

[0079] , (16);

[0080] Define nonlinear odd functions ,and:

[0081] , ,

[0082] The following restrictions must be met:

[0083] , ,remember ; This represents the coupling weight matrix. This indicates the non-periodic intermittent control input to be designed.

[0084] The target network considered in this embodiment has a dynamic model described by the following equations:

[0085] (17);

[0086] In the formula Indicates the state of the target network. , as well as Same as in equation (15), the initial state is Under these initial conditions, the system dynamics exhibit characteristics of a chaotic attractor, such as... Figure 2 As shown.

[0087] In this invention, a hybrid adversarial and cooperative topology representing the communication relationships between five follower networks is constructed. This structure can be derived from a directed graph or an undirected graph. Description (e.g.) Figure 3 ).in Represents a non-empty set of vertices. An edge set is used to characterize the relationships between network nodes.

[0088] If two nodes are connected by an edge, they are called neighbors. This represents the coupling weight matrix (i.e., the adjacency matrix), whose elements satisfy the condition that when i ≠ j, ≠0 (values ​​can be positive or negative, representing cooperation and conflict respectively); otherwise .

[0089] In this embodiment, Divided into two sets according to their cooperative and competitive relationships. , , The internal coupling weight matrices used by the five follower networks are shown below:

[0090] (18);

[0091] S2: Introduce deception attack signals.

[0092] This invention focuses on the network attack problem of the intermittent controller-actuator channel under a substitution attack. Assume the attack signal... They are independent of each other; the disturbance signal is: .

[0093] To characterize the randomness of the attack, a Bernoulli distributed random variable is introduced. The probability of a successful attack is represented by its distribution, which satisfies the following relationship:

[0094] (19);

[0095] in, It is a constant in this invention. . Represents a random variable at time t. A value of 1 indicates a probability of a successful attack. , Represents a random variable at time t. A value of 0 indicates a probability of attack failure. .

[0096] Probability of disturbance signal occurrence , , Represents the identity matrix that matches the dimension of the system.

[0097] S3: Design an aperiodic intermittent controller.

[0098] The designed non-periodic intermittent safety controller is as follows:

[0099] (20);

[0100] In the formula, , .

[0101] Furthermore, the aperiodic control interval of the coupled neural network model is as follows:

[0102] (twenty one).

[0103] In this invention, calculations can yield... , , , , , Solving linear matrix inequalities using MATLAB.

[0104] (twenty two),

[0105] (twenty three),

[0106] (twenty four),

[0107] We can obtain:

[0108] (25)

[0109] (26)

[0110] , , , , , .

[0111] According to the stability theory of hybrid systems, the binary synchronization error system formed by the follower network (Equation 15) and the target neural network (Equation 17) achieves safe and bounded stability, and the error bound is... Under the non-periodic intermittent security control method against deception attacks and random disturbances proposed in this embodiment, when a complex coupled neural network is subjected to deception attacks and disturbances, from Figure 4 The simulation results show that the states of each follower network and the target network are binaryly synchronized; the error system formed by each follower network and the target network eventually stabilizes, as shown in the figure. Figure 5 .

[0112] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A secure bisectional synchronization method based on average quasi-periodic intermittent control of coupled neural networks, characterized in that: The method comprises the following steps: S1: constructing a coupled neural network model comprising a target network and a plurality of follower networks, the coupled neural network model describing the topological structure of the networks through a symbolic weighted adjacency matrix and a Laplacian matrix, wherein the elements of the symbolic weighted adjacency matrix represent the coupling weights and properties between nodes, positive weights representing cooperative connections promoting network synchronization, and negative weights representing antagonistic connections inhibiting synchronization; the Laplacian matrix describing the net coupling input characteristics of the nodes; S2: defining a synchronization error variable between the follower networks and the target network, and establishing an error system model for describing the error dynamic evolution process between the follower networks and the target network; S3: For the system based on intermittent control, a hybrid threat modeling method between partitions is adopted: a deception attack model is introduced in the control interval, and whether the attack is successful or not is described by Bernoulli random distribution; in the non-control interval, a random disturbance model is established, and the occurrence probability of the disturbance signal is described by Bernoulli random process, and the probability of the existence of the disturbance is: where β i (t) = 1 indicates that the disturbance exists, and β i (t) = 0 indicates that there is no disturbance, ; S4: based on the hybrid system theory, the stochastic Lyapunov stability theory and the matrix inequality, a sufficient condition is derived to ensure that the error system model realizes the mean square exponential bounded stability, which is used to ensure that the coupled neural network realizes the mean square bounded two-part safe synchronization in the environment of deception attack and random disturbance; S5: designing a non-periodic intermittent safe controller suitable for the environment of deception attack and random disturbance to realize the safe synchronization control of the coupled neural network, and by reasonably configuring the gain parameters and intermittent control intervals of the controller, the synchronization error system is ensured to be mean square bounded stable, so that the mean square bounded two-part synchronization of the coupled neural network is realized in the presence of attack and disturbance; the non-periodic intermittent safe controller is: ， wherein: represents an adjustable control gain, T k is the time at which the first non-periodic intermittent control starts, is the i-th following network's i-th intermittent control width; is the i-th following network's i-th non-control width; is the control interval, is the non-control interval; constant is the coupling strength; represents the control input; In connection with step S3, the control input Further modelling under spoofing attacks and random perturbations, in particular: ， wherein: is a symbol variable, and , represents a spoofing attack signal, represents a perturbation signal.

2. The mean quasi-periodic intermittent control based coupled neural network secure bisection synchronization method of claim 1, wherein: In S1, the coupled neural network model involves the synchronization control between N follower networks and 1 target network, and the dynamic model of each follower network is given by the following formula: ， in, , Indicates the first Nodes dimensional state column vector; matrix Represents a diagonal matrix. Represents the weight matrix, and has Dimension; Represents a nonlinear odd function. Represents the transpose of a vector; Indicates about The sign function; t is the time variable; xi(t) denotes the state vector of the i-th node i (t) derivative with respect to time, i.e. rate of change of state; x i xi(t) denotes the state vector of the i-th node The mathematical model of the target network is given by the following formula: ， wherein, represents a state vector of the target network.

3. The mean quasi-periodic intermittent control based coupled neural network secure bisection synchronization method of claim 2, wherein: In S1, the topology of the coupled neural network model is represented by a directed or undirected graph. To define, where This represents a set containing N nodes. Represents an edge set. This represents a symbolically weighted adjacency matrix, whose elements are... , representing the coupling weight from node j to node i, for any ,like This indicates that from node To the node There exists a directed or undirected edge; when node With nodes When indicating a cooperative relationship In a competitive relationship When node To the node When there are no connecting edges between them ; laplacian matrix is defined as , wherein: is the degree matrix, whose diagonal elements denote the degree of node i; The Laplace matrix diagonal elements Represents the total coupling input strength of node i, off-diagonal elements This represents the coupling effect of node j on node i.

4. The mean quasi-periodic intermittent control based coupled neural network secure bisection synchronization method of claim 3, wherein: S2 is specifically: The state variable of the following network is converted into a symbolic variable is converted into ; Based on the Laplacian matrix and the odd function property, the dynamics model of the following network is organized as: ， where: denotes the first derivative of the state vector of the i-th node of the network with respect to time t after symbol transformation; denotes a vector function consisting of m non-linear odd functions, i = 1,..., m; Defining error variables between a following network and a target network and further transforming the error state to ; The two-part synchronization error system model of the follower network relative to the target network is obtained: ， wherein: represents the error vector first derivative with respect to time t; which is a nonlinear vector function of the error system model.

5. The mean quasi-periodic intermittent control based coupled neural network secure bisection synchronization method of claim 4, wherein: In S3, In the control interval, the deception attack signal is injected in the form of replacement, and whether the attack is successful or not is represented by an independent Bernoulli random variable line delineation, and: ， where: is a constant, denotes the probability that the random variable takes the value 1 at time t is equal to a constant , denotes the probability that the random variable takes the value 0 at time t is equal to a constant ; a i (t) = 1 indicates a successful attack, a i (t) = 0 indicates a failed attack.

6. The safe two-part synchronization method of the coupled neural network based on the average quasi-periodic intermittent control according to claim 5, wherein: Based on the error system model in S2 and the deception attack and random disturbance in S3, the error system model is further transformed, and the form is as follows: 。 7. The mean quasi-periodic intermittent control based coupled neural network secure bisection synchronization method of claim 6, wherein: For the network environment coexisting with deception attack and random disturbance, a non-periodic intermittent control mechanism is designed, a synchronization error system model is constructed, and based on the Lyapunov stability theory, a composite Lyapunov function is established to prove the mean square asymptotic stability or the mean square ultimate boundedness of the error system model: ， wherein denotes a weight factor, is a symmetric positive definite metric matrix used to define a quadratic norm of the error; based on which a sufficient condition is obtained to guarantee the mean-square-bounded two-sided stability of the synchronization error system model: ， ， ， wherein , denotes the minimum value of the real part of the eigenvalues of the matrix , , , , , , denotes the Laplacian matrix, denotes the control gain matrix, denotes the maximum eigenvalue of the control gain matrix , denotes a positive constant; , , , denotes a positive definite diagonal matrix, denotes the maximum eigenvalue of the F matrix, denotes the average intermittent control width, denotes the average intermittent non-control width; M is a matrix used in the Lyapunov function; ω is a weight factor in the Lyapunov function; S is a diagonal matrix whose diagonal elements are ; is a symbol variable, taking values or for describing the connection relationship of nodes in the network; , is a positive constant used in the stability condition for Lyapunov functions; λ max (F): denotes the largest eigenvalue of the positive definite diagonal matrix F.

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