Synchronization Of Reaction-diffusion Neural Networks Research Articles

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 reaction-diffusion neural networks via switched event-triggered control

A switched event-triggered strategy for the synchronization control of reaction-diffusion neural networks (RDNNs) is developed, and the trigger condition is constructed by utilizing spatial information in the domain. First, a waiting time with regard to the event-triggered mechanism is implemented to avoid the Zeno phenomenon, under which the synchronization error system is converted to a switching system. Then, using the Lyapunov function, the Poincare's inequality and the free weighting matrix method, a sufficient condition for the exponential synchronization of RDNNs is given. Subsequently, an event-triggered controller is designed by virtue of the linear matrix inequalities. This method is also extended to deal with the synchronization of uncertain RDNNs. Finally, simulation examples illustrate our results.

Stability Analysis of Second-Order Linear PDEs on Time Scales

This paper presents the stability analysis of a class of second-order linear partial differential equations (PDEs) on time scales with diffusion operator and first-order partial derivative. According to the time scale theory, the Lyapunov functional method, and some inequality techniques, sufficient conditions for exponential stability are strictly obtained, and the results are generalized for that where both the discrete-time and continuous-time cases are considered jointly. In addition, the theoretical results are applied to exponential synchronization of reaction-diffusion neural networks (RDNNs). Simulation examples are given to verify the feasibility of our results.

Switching synchronization of reaction-diffusion neural networks with time-varying delays

This paper explores the switching synchronization problem of reaction-diffusion neural networks with time-varying delays, and two improved synchronization switching law strategies are proposed for stability analysis. One is constructed by adopting a Lyapunov-Krasovskii functional combined with the use of improved Wirtinger's integral inequality for managing the reaction-diffusion terms. The other is designed to utilize the Lyapunov-Razumikhin function, which is easier to deal with the reaction-diffusion terms directly compared to the former one. As a result, the time-space feature of the proposed switching synchronization is more robust and compatible than previous works. Finally, the simulated numerical experiments make out the effectiveness of the developed approaches in this work.

Synchronization of Reaction-Diffusion Neural Networks with Sampled-Data Control Via a New Two-Sided Looped Functional

Synchronization of Reaction-Diffusion Neural Networks with Sampled-Data Control Via a New Two-Sided Looped Functional

Finite-time synchronization of reaction-diffusion neural networks with time-varying parameters and discontinuous activations

The issue of finite-time synchronization (FTS) of discontinuous reaction-diffusion neural networks (DRDNNs) with time-varying coefficients is investigated here. First, the effects caused by discontinuous activations are handled by differential inclusion theory. Secondly, a relaxed Lyapunov function (RLF) method is introduced to design novel control algorithms, including state-feedback control and adaptive control, to achieve FTS of DRDNNs, and the upper-bound of the settling time is explicitly estimated. In this RLF method, the LF is allowed to be nonsmooth and possess an indefinite derivative.Moreover, the FTS results via generalized pinning state-feedback and generalized pinning adaptive control are presented as two corollaries. Finally, two numerical simulations are presented to substantiate the merits of the obtained results.

Adaptive Event-Triggered Synchronization of Reaction-Diffusion Neural Networks.

This article focuses on the design of an adaptive event-triggered sampled-data control (ETSDC) mechanism for synchronization of reaction-diffusion neural networks (RDNNs) with random time-varying delays. Different from the existing ETSDC schemes with predetermined constant thresholds, an adaptive ETSDC mechanism is proposed for RDNNs. The adaptive ETSDC mechanism can be promptly adaptively adjusted since the threshold function is based on the current sampled and latest transmitted signals. Thus, the adaptive ETSDC mechanism can effectively save communication resources for RDNNs. By taking the influence of uncertain factors, the random time-varying delays are considered, which belongs to two intervals in a probabilistic way. Then, by constructing an appropriate Lyapunov-Krasovskii functional (LKF), new synchronization criteria are derived for RDNNs. By solving a set of linear matrix inequalities (LMIs), the desired adaptive ETSDC gain is obtained. Finally, the merits of the adaptive ETSDC mechanism and the effectiveness of the proposed results are verified by one numerical example.

Synchronization for hybrid coupled reaction-diffusion neural networks with stochastic disturbances via spatial sampled-data control strategy

The synchronization of reaction-diffusion neural networks with state and spatial couplings is investigated in this article, and the time-varying delay and stochastic disturbances are considered in the proposed systems. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Here, we suggest a spatial sampled-data controller design, where the sampled-data (in space) measurements of the state are taken in a finite number of fixed sampling points in the spatial domain. It is assumed that the sampling intervals in space are bounded. Based on the Lyapunov stability theory, Young’s and Wirtinger’s inequalities techniques, some sufficient conditions are presented to synchronize the hybrid coupling reaction-diffusion neural networks with stochastic disturbances. Finally, the efficiency of the derived criteria will be demonstrated by resorting to two numerical examples.

Boundary Control for Exponential Synchronization of Reaction-Diffusion Neural Networks Based on Coupled PDE-ODEs

Abstract This paper studies synchronization and exponential synchronization of reaction-diffusion neural networks based on semi-linear coupled partial differential equations-ordinary differential equations. Two kinds of boundary control methods are studied, one collocated boundary measurement based form and the other distributed measurement based form. Sufficient conditions for existence of the two proposed boundary controllers for synchronization and exponential synchronization are respectively obtained in terms of LMIs. Two examples are given to show the effectiveness of the proposed boundary control.

Pinning synchronization for reaction-diffusion neural networks with delays by mixed impulsive control

The synchronization for reaction-diffusion neural networks with time-varying and distributed delays is concerned in the letter. A mixed pinning impulsive controller is introduced for realizing the synchronization of the neural networks. The novel control method combines the advantages of pinning control as well as two types of impulsive effects (i.e. synchronizing and desynchronizing impulses) such that the control cost is reduced tremendously in practical applications. By applying the generalized comparison principle and average mixed impulsive interval approach, some sufficient criteria are constructed so that response system can be synchronized with corresponding drive system. Finally, two numerical examples are presented to verify the correctness of the obtained results.

Adaptive Synchronization of Reaction-Diffusion Neural Networks and Its Application to Secure Communication.

This paper is mainly concerned with the synchronization problem of reaction-diffusion neural networks (RDNNs) with delays and its direct application in image secure communications. An adaptive control is designed without a sign function in which the controller gain matrix is a function of time. The synchronization criteria are established for an error model derived from master-slave models through solving the set of linear matrix inequalities derived by constructing the suitable novel Lyapunov-Krasovskii functional candidate, Green's formula, and Wirtinger's inequality. If the proposed sufficient conditions are satisfied, then the global asymptotic synchronization of the error model is guaranteed. The numerical illustrations are provided to demonstrate the validity of the derived synchronization criteria. In addition, the role of system parameters is picturized through the chaotic nature of RDNNs and those unprecedented solutions is utilized to promote better security of image transactions. As is evident, the enhancement of image encryption algorithm is designed with two levels, namely, image watermarking and diffusion process. The contributions of this paper are discussed as concluding remarks.

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.

Pinning Impulsive Synchronization of Reaction-Diffusion Neural Networks With Time-Varying Delays.

This paper investigates the exponential synchronization of reaction-diffusion neural networks with time-varying delays subject to Dirichlet boundary conditions. A novel type of pinning impulsive controllers is proposed to synchronize the reaction-diffusion neural networks with time-varying delays. By applying the Lyapunov functional method, sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction-diffusion neural networks with large and small delay sizes. It is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network; the technique used in this paper is also applicable to reaction-diffusion networks with Neumann boundary conditions. Numerical examples are presented to demonstrate the effectiveness of the theoretical results.

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 of Reaction-Diffusion Neural Networks with Mixed Time-Varying Delays

This paper treats of the synchronization issue for reaction-diffusion neural networks with mixed time-varying delays. State feedback and adaptive controllers are designed, respectively, such that the response system can be synchronized with corresponding drive system. In addition, when the external disturbances appear in the networks, an adaptive controller is designed to guarantee the $$H_\infty $$ synchronization for the networks. Two numerical examples are presented to show the effectiveness of our proposed methods.

Exponential synchronization for reaction-diffusion neural networks with mixed time-varying delays via periodically intermittent control

This paper deals with the exponential synchronization problem for reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance. By using stochastic analysis approaches and constructing a novel Lyapunov–Krasovskii functional, a periodically intermittent controller is first proposed to guarantee the exponential synchronization of reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance in terms of p-norm. The obtained synchronization results are easy to check and improve upon the existing ones. Particularly, the traditional assumptions on control width and time-varying delays are removed in this paper. This paper also presents two illustrative examples and uses simulated results of these examples to show the feasibility and effectiveness of the proposed scheme.