Stability of stochastic impulsive reaction–diffusion neural networks with S-type distributed delays and its application to image encryption

Finite-Time Boundedness of Impulsive Delayed Reaction-Diffusion Stochastic Neural Networks

Considering the impulsive delayed reaction-diffusion stochastic neural networks (IDRDSNNs) with hybrid impulses, the finite-time boundedness (FTB) and finite-time contractive boundedness (FTCB) are investigated in this article. First, a novel delay integral inequality is presented. By integrating this inequality with the comparison principle, some sufficient conditions that ensure the FTB and FTCB of IDRDSNNs are obtained. This study demonstrates that the FTB of neural networks with hybrid impulses can be maintained, even in the presence of impulsive perturbations. And for a system that is not FTB due to impulsive perturbations, achieving FTB is possible through the implementation of appropriate impulsive control and optimization of the average impulsive intervals. In addition, to validate the practicality of our results, three illustrative examples are provided. In the end, these theoretical findings are successfully applied to image encryption.

Fixed-time synchronization of delayed multiple inertial neural network with reaction-diffusion terms under cyber-physical attacks using distributed control and its application to multi-image encryption

This study examines the fixed-time synchronization (FXTS) problem of delayed multiple inertial neural networks (MINNs) against cyber-physical attacks (CPA) execute an uncertain impulse, using reaction-diffusion (RD) terms. Using fixed-time stability theory, the paper derives innovative and practical criteria for FXTS. It also introduces a MINNs to counteract CPA by executing uncertain impulses with RD terms. Designing security control laws for MINNS with RD terms poses significant challenges, particularly when these networks are tasked with cooperative functions in the presence of failures or attacks. A distributed control strategy is introduced to attain FXTS for the delayed MINNs incorporating RD terms. To examine the consequences of CPA, we will build a Lyapunov function and combine it with some M-matrix properties. Additionally, a security control law is provided to guarantee the FXTS of the consider NN system. The demonstrated settling time (ST) of the designated MINNs is provided. From an algorithmic perspective, it is notable that the security framework and control algorithm are designed to select parameters for the feedback gain matrix and coupling strength to achieve synchronization. A numerical model is provided to support the obtained theoretical findings. Finally, our proposition of a multi-image encryption algorithm, utilizing MINNs and secured by robust security protocols, serves to uphold the integrity of electronic healthcare systems, ensuring the safeguarding of sensitive medical data.

Exponential Synchronization Control of Reaction-Diffusion Fuzzy Memristive Neural Networks: Hardy-Poincarè Inequality

This article is devoted to solving the exponential synchronization problem of a new type of fuzzy memristive neural network with reaction-diffusion terms. By introducing adaptive laws, two controllers are designed. After combining the inequality technique with the Lyapunov function approach, some easily verified sufficient conditions are established to ensure the exponential synchronization of the reaction-diffusion fuzzy memristive system under the proposed adaptive scheme. In addition, by using the Hardy-Poincarè inequality, the diffusion terms are estimated associated with the information of the reaction-diffusion coefficients and the regional feature, which improves some existing conclusions. Finally, an illustrative example is presented to demonstrate the validity of the theoretical results.

Fast synchronization control and application for encryption-decryption of coupled neural networks with intermittent random disturbance

In this paper, we design a new class of coupled neural networks with stochastically intermittent disturbances, in which the perturbation mechanism is different from other existed random neural networks. It is significant to construct the new models, which can simulate a class of the real neural networks in the disturbed environment, and the fast synchronization control strategies are studied by an adjustable parameter α. A controller with coupling signal is designed to study the exponential synchronization problem, meanwhile, another effective controller with not only adjustable synchronization rate but also with infinite gain avoided is used to investigate the preset-time synchronization. The fast synchronization conditions have been obtained by Lyapunov stability principle, Laplacian matrix and some inequality techniques. A numerical example shows the effectiveness of the control schemes, and the different control factors for synchronization rate are given to discuss the control effect. In particular, the image encryption-decryption based on drive-response networks has been successfully applied.

Fixed-time synchronization of complex-valued neural networks for image protection and 3D point cloud information protection

This paper studies the fixed-time synchronization (FDTS) of complex-valued neural networks (CVNNs) based on quantized intermittent control (QIC) and applies it to image protection and 3D point cloud information protection. A new controller was designed which achieved FDTS of the CVNNs, with the estimation of the convergence time not dependent on the initial state. Our approach divides the neural network into two real-valued systems and then combines the framework of the Lyapunov method to give criteria for FDTS. Applying synchronization to image protection, the image will be encrypted with a drive system sequence and decrypted with a response system sequence. The quality of image encryption and decryption depends on the synchronization error. Meanwhile, the depth image of the object is encrypted and then the 3D point cloud is reconstructed based on the decrypted depth image. This means that the 3D point cloud information is protected. Finally, simulation examples verify the efficacy of the controller and the synchronization criterion, giving results for applications in image protection and 3D point cloud information protection.

Predefined-time synchronization of coupled neural networks with switching parameters and disturbed by Brownian motion

This article focuses on predefined time synchronization problem for a class of signal switching neural networks with time-varying delays. In the network models, we not only consider the coupling characteristics in the following networks, but also consider the disturbance with standard Brownian motion. In the design of the controller, the control gain is designed as 1ɛ+T_p-t (t∈[T₀,T_p), ɛ is an optional smaller positive number), which avoids the infinite gain (the control gain is designed as 1T_p-t in other reference). In order to get the predefined time control law, a power function is multiplied to the Lyapunov functional, from which it can get an exponential upper bound function via the derivative and mathematical expectation operation. Utilizing the martingale theory and the method of Laplace matrix, some novel predefined time synchronization criteria are obtained for the leader-following neural networks, meanwhile the following networks can maintain the leader network after achieved synchronization. Based on the special network of the main system, five corollaries separately develop the predefined time synchronization results from different perspectives. An example with some simulation figures and computing results fully exhibits the effectiveness of the achieved synchronization scheme. In this case, although the error signal is disturbed by Brownian motion, the trace signal can still stably converge to zero by this control scheme, meanwhile the predefined-time control effect is achieved.

Event-triggered H∞/passive synchronization for Markov jumping reaction-diffusion neural networks under deception attacks

The issue of H_∞/passive master-slave synchronization for Markov jumping neural networks with reaction-diffusion terms is investigated in this paper via an event-triggered control scheme under deception attacks. To lighten the burden of limited communication bandwidth as well as ensure the control performance, an event-triggered transmission scheme is developed. Meanwhile, the randomly occurring deception attacks, which received from the event generator are assumed to modify the sign of the control signal, are taken into account. Furthermore, sufficient conditions ensuring the prescribed H_∞/passive performance level of the neural networks, are deduced beyond Lyapunov stability theory, and the controller gains are derived dealing with the matrix convex optimization problem. At last, the availability of the approach proposed is demonstrated via a numerical example.

Practical Exponential Stability of Impulsive Stochastic Reaction-Diffusion Systems With Delays

This article studies the practical exponential stability of impulsive stochastic reaction-diffusion systems (ISRDSs) with delays. First, a direct approach and the Lyapunov method are developed to investigate the p th moment practical exponential stability and estimate the convergence rate. Note that these two methods can also be used to discuss the exponential stability of systems in certain conditions. Then, the practical stability results are successfully applied to the impulsive reaction-diffusion stochastic Hopfield neural networks (IRDSHNNs) with delays. By the illustration of four numerical examples and their simulations, our results in this article are proven to be effective in dealing with the problem of practical exponential stability of ISRDSs with delays, and may be regarded as stabilization results.

Fixed-Time Synchronization of Neural Networks Based on Quantized Intermittent Control for Image Protection

This paper considers the fixed-time synchronization (FIXTS) of neural networks (NNs) by using quantized intermittent control (QIC). Based on QIC, a fixed-time controller is designed to ensure that the NNs achieve synchronization in finite time. With this controller, the settling time can be estimated regardless of initial conditions. After ensuring that the system has stabilized through this strategy, it is suitable for image protection given the behavior of the system. Meanwhile, the encryption effect of the image depends on the encryption algorithm, and the quality of the decrypted image depends on the synchronization error of NNs. The numerical results show that the designed controller is effective and validate the practical application of FIXTS of NNs in image protection.

Exponential synchronization of coupled neural networks under stochastic deception attacks

In this paper, the issue of synchronization is investigated for coupled neural networks subject to stochastic deception attacks. Firstly, a general differential inequality with delayed impulses is given. Then, the established differential inequality is further extended to the case of delayed stochastic impulses, in which both the impulsive instants and impulsive intensity are stochastic. Secondly, by modeling the stochastic discrete-time deception attacks as stochastic impulses, synchronization criteria of the coupled neural networks under the corresponding attacks are given. Finally, two numerical examples are provided to demonstrate the correctness of the theoretical results.

Gain-Scheduled Finite-Time Synchronization for Reaction-Diffusion Memristive Neural Networks Subject to Inconsistent Markov Chains

An innovative class of drive-response systems that are composed of Markovian reaction-diffusion memristive neural networks, where the drive and response systems follow inconsistent Markov chains, is proposed in this article. For this kind of nonlinear parameter-varying systems, a suitable gain-scheduled controller that involves a mode and memristor-dependent item is designed, so that the error system is bounded within a finite-time interval. Moreover, by constructing a novel Lyapunov-Krasovskii functional and employing the canonical Bessel-Legendre inequality and free-weighting matrix method, the conservatism of the finite-time synchronization criterion can be greatly reduced. Finally, two numerical examples are provided to illustrate the feasibility and practicability of the obtained results.

Multi-periodicity of switched neural networks with time delays and periodic external inputs under stochastic disturbances

This paper presents new theoretical results on the multi-periodicity of recurrent neural networks with time delays evoked by periodic inputs under stochastic disturbances and state-dependent switching. Based on the geometric properties of activation function and switching threshold, the neuronal state space is partitioned into 5ⁿ regions in which 3ⁿ ones are shown to be positively invariant with probability one. Furthermore, by using Itô's formula, Lyapunov functional method, and the contraction mapping theorem, two criteria are proposed to ascertain the existence and mean-square exponential stability of a periodic orbit in every positive invariant set. As a result, the number of mean-square exponentially stable periodic orbits increases to 3ⁿ from 2ⁿ in a neural network without switching. Two illustrative examples are elaborated to substantiate the efficacy and characteristics of the theoretical results.

Impulsive Synchronization of Unbounded Delayed Inertial Neural Networks With Actuator Saturation and Sampled-Data Control and its Application to Image Encryption

The article considers the impulsive synchronization for inertial neural networks with unbounded delay and actuator saturation via sampled-data control. Based on an impulsive differential inequality, the difficulties caused by unbounded delay and impulsive effect may be effectively avoid. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequality (LMI) criteria that guarantee asymptotical synchronization for the considered model via hybrid control are given. As special cases, the asymptotical synchronization of the considered model via sampled-data control and saturating impulsive control are also studied, respectively. Numerical simulations are presented to claim the effectiveness of theoretical analysis. A new image encryption algorithm is proposed to utilize the synchronization theory of hybrid control. The validity of image encryption algorithm can be obtained by experiments.

Exponential Synchronization of Delayed Memristor-Based Uncertain Complex-Valued Neural Networks for Image Protection

This article solves the exponential synchronization issue of memristor-based complex-valued neural networks (MCVNNs) with time-varying uncertainties via feedback control. Compared with the traditional control methods, a more practical and general control scheme with the available uncertain information of the parameters is newly developed for MCVNNs. Our approach considers the proposed neural networks as two dynamic real-valued systems. Then, the less conservative exponential synchronization criteria are proposed by incorporating the framework of the Lyapunov method and inequality techniques. Under the proposed algorithm, not only can the stability of MCVNNs be guaranteed but also the behavior of such a system is appropriate for image protection. Meanwhile, the sensitive measure of the encryption and decryption can be converted into synchronization error. When monitoring the secure mechanism as a whole, the influence of error feasible domain on image decryption is analyzed. Simulation examples are provided to verify the efficacy of the proposed synchronization criterion and the results of practical application on image protection.

A new Lyapunov functional for stability analysis of neutral-type Hopfield neural networks with multiple delays

This research paper conducts an investigation into the stability issue for a more general class of neutral-type Hopfield neural networks that involves multiple time delays in the states of neurons and multiple neutral delays in the time derivatives of the states of neurons. By constructing a new proper Lyapunov functional, an alternative easily verifiable algebraic criterion for global asymptotic stability of this type of Hopfield neural systems is derived. This new stability condition is entirely independent of time and neutral delays. Two instructive examples are employed to indicate that the result obtained in this paper reveals a new set of sufficient stability criteria when it is compared with the previously reported stability results. Therefore, the proposed stability result enlarges the application domain of Hopfield neural systems of neutral types.

General decay synchronization and H∞ synchronization of spatial diffusion coupled delayed reaction-diffusion neural networks

This paper deals with the general decay synchronization (GDS) and general decay H_∞ synchronization (GDHS) problems for spatial diffusion coupled delayed reaction-diffusion neural networks (SDCDRDNNs) without and with uncertain parameters respectively. First, based on the ψ-type stability and ψ-type function, the concept of GDS is generalized to include general robust decay synchronization (GRDS) and GDHS. Then, by exploiting a nonlinear controller and different types of inequality techniques, some verifiably sufficient conditions ensuring the GDS and GDHS of SDCDRDNNs (without and with uncertain parameters) are derived. Finally, two simulative examples are provided to demonstrate the validity of the synchronization results obtained.

pth Moment Stability of a Stationary Solution for a Reaction Diffusion System with Distributed Delays

In this paper, the Sobolev embedding theorem, Holder inequality, the Lebesgue contrl convergence theorem, the operator norm estimation technique, and critical point theory are employed to prove the existence of nontrivial stationary solution for p-Laplacian diffusion system with distributed delays. Furthermore, by giving the definition of pth moment stability, the authors use the Lyapunovfunctional method and Kamke function to derive the stability of nontrivialstationary solution. Moreover, a numerical example illuminates the effectiveness of the proposed methods. Finally, an interesting further thought is put forward, which is conducive to the in-depth study of the problem.