Exponential synchronization for reaction–diffusion networks with mixed delays in terms of -norm via intermittent driving

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.

Adaptive Synchronization of Reaction-Diffusion Neural Networks With Nondifferentiable Delay via State Coupling and Spatial Coupling

In this article, master-slave synchronization of reaction-diffusion neural networks (RDNNs) with nondifferentiable delay is investigated via the adaptive control method. First, centralized and decentralized adaptive controllers with state coupling are designed, respectively, and a new analytical method by discussing the size of adaptive gain is proposed to prove the convergence of the adaptively controlled error system with general delay. Then, spatial coupling with adaptive gains depending on the diffusion information of the state is first proposed to achieve the master-slave synchronization of delayed RDNNs, while this coupling structure was regarded as a negative effect in most of the existing works. Finally, numerical examples are given to show the effectiveness of the proposed adaptive controllers. In comparison with the existing adaptive controllers, the proposed adaptive controllers in this article are still effective even if the network parameters are unknown and the delay is nonsmooth, and thus have a wider range of applications.

Exponential Synchronization of Memristor-Based Competitive Neural Networks With Reaction-Diffusions and Infinite Distributed Delays

Taking into account the infinite distributed delays and reaction-diffusions, this article investigates the global exponential synchronization problem of a class of memristor-based competitive neural networks (MCNNs) with different time scales. Based on the Lyapunov-Krasovskii functional and inequality approach, an adaptive control approach is proposed to ensure the exponential synchronization of the addressed drive-response networks. The closed-loop system is a discontinuous and delayed partial differential system in a cascade form, involving the spatial diffusion, the infinite distributed delays, the parametric adaptive law, the state-dependent switching parameters, and the variable structure controllers. By combining the theories of nonsmooth analysis, partial differential equation (PDE) and adaptive control, we present a new analytical method for rigorously deriving the synchronization of the states of the complex system. The derived m-norm (m ≥ 2)-based synchronization criteria are easily verified and the theoretical results are easily extended to memristor-based neural networks (NNs) without different time scales and reaction-diffusions. Finally, numerical simulations are presented to verify the effectiveness of the theoretical results.

Intermittent boundary stabilization of stochastic reaction-diffusion Cohen-Grossberg neural networks

Cohen-Grossberg neural networks (CGNNs) play an important role in many applications and the stabilization of this system has been well studied. This study considers the exponential stabilization for stochastic reaction-diffusion Cohen-Grossberg neural networks (SRDCGNNs) by means of an aperiodically intermittent boundary control. Both SRDCGNNs without and with time-delays are discussed. By employing the spatial integral functional method and Poincare's inequality, criteria are derived to ensure the controlled systems achieve mean square exponential stabilization. Based on these criteria, the effects of diffusion item, control gains, the minimum control proportion and time-delays on exponential stability are analyzed. Examples are given to illustrate the effectiveness of the obtained theoretical results.

Spacial sampled-data control for H∞ output synchronization of directed coupled reaction-diffusion neural networks with mixed delays

This work investigates the H_∞ output synchronization (HOS) of the directed coupled reaction-diffusion (R-D) neural networks (NNs) with mixed delays. Firstly, a model of the directed state coupled R-D NNs is introduced, which not only contains some discrete and distributed time delays, but also obeys a mixed Dirichlet-Neumann boundary condition. Secondly, a spacial sampled-data controller is proposed to achieve the HOS of the considered networks. This type of controller can reduce the update rate in the process of control by measuring the state of networks at some fixed sampling points in the space region. Moreover, some criteria for the HOS are established by designing an appropriate Lyapunov functional, and some quantitative relations between diffusion coefficients, mixed delays, coupling strength and control parameters are given accurately by these criteria. Thirdly, the case of directed spatial diffusion coupled networks is also studied and, the following finding is obtained: the spatial diffusion coupling can suppress the HOS while the state coupling can promote it. Finally, one example is simulated as the verification of the theoretical results.

Synchronization of coupled stochastic complex-valued dynamical networks with time-varying delays via aperiodically intermittent adaptive control

This paper deals with the synchronization problem of a class of coupled stochastic complex-valued drive-response networks with time-varying delays via aperiodically intermittent adaptive control. Different from the previous works, the intermittent control is aperiodic and adaptive, and the restrictions on the control width and time delay are removed, which lead to a larger application scope for this control strategy. Then, based on the Lyapunov method and Kirchhoff's Matrix Tree Theorem as well as differential inequality techniques, several novel synchronization conditions are derived for the considered model. Specially, impulsive control is also considered, which can be seen as a special case of the aperiodically intermittent control when the control width tends to zero. And the corresponding synchronization criteria are given as well. As an application of the theoretical results, a class of stochastic complex-valued coupled oscillators with time-varying delays is studied, and the numerical simulations are also given to demonstrate the effectiveness of the control strategies.

Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays

This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.

Exponential synchronization of generalized neural networks with mixed time-varying delays and reaction-diffusion terms via aperiodically intermittent control

In this paper, the exponential synchronization problem of generalized reaction-diffusion neural networks with mixed time-varying delays is investigated concerning Dirichlet boundary conditions in terms of p-norm. Under the framework of the Lyapunov stability method, stochastic theory, and mathematical analysis, some novel synchronization criteria are derived, and an aperiodically intermittent control strategy is proposed simultaneously. Moreover, the effects of diffusion coefficients, diffusion space, and stochastic perturbations on the synchronization process are explicitly expressed under the obtained conditions. Finally, some numerical simulations are performed to illustrate the feasibility of the proposed control strategy and show different synchronization dynamics under a periodically/aperiodically intermittent control.

Impulsive Synchronization of Reaction-Diffusion Neural Networks With Mixed Delays and Its Application to Image Encryption

This paper presents a new impulsive synchronization criterion of two identical reaction-diffusion neural networks with discrete and unbounded distributed delays. The new criterion is established by applying an impulse-time-dependent Lyapunov functional combined with the use of a new type of integral inequality for treating the reaction-diffusion terms. The impulse-time-dependent feature of the proposed Lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction-diffusion neural networks than the conventional impulse-time-independent Lyapunov functions/functionals, while the new integral inequality, which is derived from Wirtinger's inequality, overcomes the conservatism introduced by the integral inequality used in the previous results. Numerical examples demonstrate the effectiveness of the proposed method. Later, the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image. The experimental results verify that the proposed image-encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks.

Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control

In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.

Fully parallel write/read in resistive synaptic array for accelerating on-chip learning

A neuro-inspired computing paradigm beyond the von Neumann architecture is emerging and it generally takes advantage of massive parallelism and is aimed at complex tasks that involve intelligence and learning. The cross-point array architecture with synaptic devices has been proposed for on-chip implementation of the weighted sum and weight update in the learning algorithms. In this work, forming-free, silicon-process-compatible Ta/TaOx/TiO2/Ti synaptic devices are fabricated, in which >200 levels of conductance states could be continuously tuned by identical programming pulses. In order to demonstrate the advantages of parallelism of the cross-point array architecture, a novel fully parallel write scheme is designed and experimentally demonstrated in a small-scale crossbar array to accelerate the weight update in the training process, at a speed that is independent of the array size. Compared to the conventional row-by-row write scheme, it achieves >30× speed-up and >30× improvement in energy efficiency as projected in a large-scale array. If realistic synaptic device characteristics such as device variations are taken into an array-level simulation, the proposed array architecture is able to achieve ∼95% recognition accuracy of MNIST handwritten digits, which is close to the accuracy achieved by software using the ideal sparse coding algorithm.

Synchronization of linearly coupled networks with delays via aperiodically intermittent pinning control

In this paper, we investigate the exponential synchronization problem for linearly coupled networks with delay by pinning a simple aperiodically intermittent controller. The network topology can be directed. Different from previous works, the intermittent control can be aperiodic. Two types of delay are considered. The first case is that the delay is time-varying and large, and in this case, there is no restriction imposed on the delay and the control (and/or rest) width. The other one is that the delay is small enough so that it is less than the minimum of control width. Different approaches are provided to investigate these two cases, and some criteria are given to realize exponential synchronization. Furthermore, by applying the adaptive approach to the second model, we establish a general adaptive theory for intermittent control, which can be applied not only to networks without time delay, but also to delayed networks, regardless of whether the intermittent control is periodic or aperiodic. Finally, the numerical simulations are given to verify the validness of the theoretical results.

Synchronization of nonlinear coupled networks via aperiodically intermittent pinning control

In this paper, pinning synchronization problem for nonlinear coupled networks is investigated, which can be recurrently connected neural networks, cellular neural networks, Hodgkin-Huxley models, Lorenz chaotic oscillators, and so on. Nodes in the network are assumed to be identical and nodes' dynamical behaviors are described by continuous-time equations. The network topology is undirected and static. At first, the scope of accepted nonlinear coupling functions is defined, and the effect of nonlinear coupling functions on synchronization is carefully discussed. Then, the pinning control technique is used for synchronization, especially the control type is aperiodically intermittent. Some sufficient conditions to guarantee global synchronization are presented. Furthermore, the adaptive approach is also applied on the pinning control, and a centralized adaptive algorithm is designed and its validity is also proved. Finally, several numerical simulations are given to verify the obtained theoretical results.

Synchronization in output-coupled temporal Boolean networks

This paper presents an analytical study of synchronization in an array of output-coupled temporal Boolean networks. A temporal Boolean network (TBN) is a logical dynamic system developed to model Boolean networks with regulatory delays. Both state delay and output delay are considered, and these two delays are assumed to be different. By referring to the algebraic representations of logical dynamics and using the semi-tensor product of matrices, the output-coupled TBNs are firstly converted into a discrete-time algebraic evolution system, and then the relationship between the states of coupled TBNs and the initial state sequence is obtained. Then, some necessary and sufficient conditions are derived for the synchronization of an array of TBNs with an arbitrary given initial state sequence. Two numerical examples including one epigenetic model are finally given to illustrate the obtained results.