Coupled Reaction-diffusion Neural Networks Research Articles

Event-triggered passivity and synchronization of multiple derivative coupled reaction–diffusion neural networks

The paper studies the event-triggered passivity and synchronization problems for multiple derivative coupled reaction–diffusion neural networks. Two types of multiple derivative coupled reaction–diffusion neural networks, with and without time-varying delay, are considered. According to the characteristics of multiple derivative coupled reaction–diffusion neural networks, an event-triggered condition is constructed. By imposing appropriate Lyapunov functionals and inequality techniques, several passivity conditions are established for these two networks under the designed event-triggered controllers. Then, synchronization criteria of these two networks are derived based on the relationship between output-strict passivity and synchronization. Moreover, the non-occurrence of the Zeno behavior in the proposed control is proved. Numerical example is illustrated to verify the effectiveness of the proposed criteria. Finally, theoretical results and the associated image encryption application are validated through numerical simulations and statistical analyses.

Observer-Based Boundary Stabilization of Coupled Semilinear Reaction-Diffusion Neural Networks With Spatially Varying Coefficients via Event-Triggered Controller.

The aim of this article is to propose an observer-based event-triggered Robin boundary control strategy for the exponential stabilization of the coupled semilinear reaction-diffusion neural networks with spatially varying coefficients. Toward this aim, we design an observer to estimate the value of system states by using some of these system values as the available measurement. An observer-based event-triggered boundary stabilizer is then presented to exponentially stabilize the considered systems with the Zeno behavior being excluded. Throughout this article, the main used method is backstepping, which yields an explicit expression of the control formulae. Moreover, we see that the proposed event-triggered boundary control scheme can ensure the desired level of control performance with fewer control law updates. A numerical example is finally given to illustrate the effectiveness of our proposed method.

Finite-Time Output Synchronization of Multiple Weighted Reaction-Diffusion Neural Networks With Adaptive Output Couplings.

This article mainly considers the output synchronization (OS) problem of multiple weighted and adaptive output coupled reaction-diffusion neural networks (RDNNs) without and with coupling delays in finite time. Without coupling delays, an adaptive control law and an output feedback controller are, respectively, proposed to ensure that the multiple weighted and output coupled RDNNs are output synchronized and output synchronized in finite time. With coupling delays, an adaptive coupling weights control scheme and a novel feedback controller are put forward to make the multiple weighted RDNNs with output couplings achieve OS in finite time. Moreover, the finite-time OS is considered in the presence of external disturbances. By the Lyapunov approach, several finite-time OS and OS criteria are given. Finally, two simulation examples are presented to justify the effectiveness of the proposed adaptive control laws and controllers.

Event-triggered pinning passivity and synchronization of multiple spatial diffusion coupled reaction–diffusion neural networks

In this paper, the problem of the event-triggered pinning passivity and synchronization for multiple spatial diffusion coupled reaction–diffusion neural networks is investigated. Two types of multiple spatial diffusion coupled reaction–diffusion neural networks, with undirected and directed topologies, are considered. Combining the advantages of event-triggered and pinning control methods, event-triggered pinning controllers for these two networks are constructed. By imposing appropriate Lyapunov functionals and inequality techniques, several passivity and synchronization conditions are established for these two networks under the designed event-triggered pinning controllers. Moreover, the non-occurrence of the Zeno behavior in the proposed control is proved. Two numerical examples are illustrated to verify the effectiveness of the proposed criteria.

Event-triggered impulsive cluster synchronization of coupled reaction–diffusion neural networks and its application to image encryption

This paper investigates the cluster synchronization of coupled neural networks with reaction–diffusion terms. With the help of impulsive control strategies, some cluster synchronization criteria are proposed by an appropriate event-triggered mechanism. A numerical example is given to verify the validity of the theoretical results. Additionally, the proposed event-triggered impulsive synchronization is successfully applied to image encryption with encouraging cryptanalysis results demonstrating its strong ability to efficiently encrypt images.

Pinning Spatiotemporal Sampled-Data Synchronization of Coupled Reaction-Diffusion Neural Networks Under Deception Attacks.

In this article, we investigate the pinning spatiotemporal sampled-data (SD) synchronization of coupled reaction-diffusion neural networks (CRDNNs), which are directed networks with SD in time and space communications under random deception attacks. In order to handle with the random deception attacks, we establish a directed CRDNN model, which respects the impacts of variable sampling and random deception attacks within a unified framework. Through the designed pinning spatiotemporal SD controller, sufficient conditions are obtained by linear matrix inequalities (LMIs) that guarantee the mean square exponential stability of the synchronization error system (SES) derived by utilizing inequality techniques, the stochastic analysis technique, and Lyapunov-Krasovskii functional (LKF). Finally, a numerical example is utilized to support the presented pinning spatiotemporal SD synchronization method.

Robust H∞ Pinning Synchronization for Multiweighted Coupled Reaction-Diffusion Neural Networks.

This article focuses on the robust H∞ synchronization of two types of coupled reaction-diffusion neural networks with multiple state and spatial diffusion couplings by utilizing pinning adaptive control strategies. First, based on the Lyapunov functional combined with inequality techniques, several sufficient conditions are formulated to ensure H∞ synchronization for these two networks with parameter uncertainties. Moreover, node-based pinning adaptive control strategies are devised to address the robust H∞ synchronization problem. In addition, some criteria of H∞ synchronization for these two networks under parameter uncertainties are developed via edge-based pinning adaptive controllers. Finally, two numerical examples are presented to verify our results.

Synchronization and control for directly coupled reaction–diffusion neural networks with multiweights and hybrid coupling

This paper mainly deals with the synchronization and pinning control for multiweighted, directly, and hybridly coupled reaction–diffusion neural networks (MDHCRDNNs). Different communication channels are expressed by multiple coupling matrices, while hybrid coupling means that state information combined with spatial diffusion information are employed jointly to attain synchronization. In comparison to previously published literature on multiweighted networks, outer matrices (OMs) in our paper can be directly coupled, with negative elements, and not even connected. One novel synchronization strategy is proposed to address directed networks with multiweights by integrating state matrices and spatial matrices into new union matrices. Then, for MDHCRDNNs, we obtain if the weighted groups of added OMs for each dimension are strongly connected, then synchronization and pinning synchronization criteria are derived. Furthermore, synchronization for adaptive coupling strength is solved as well. Finally, the effectiveness of these obtained results is verified through simulation examples.

Quantized pinning bipartite synchronization of fractional-order coupled reaction–diffusion neural networks with time-varying delays

Neural synchronization not only has a significant theoretical role for understanding brain function, but also is important for artificial neural network development. In this paper, a novel and more general directed signed network model, consisting of a set of fractional reaction–diffusion delay neural networks, is articulated. Moreover, we also consider the coexistence of cooperation and competition as a coupling scheme among neurons, which is a mechanism found in biological neural interactions. By designing a new quantized pinning controller based on depth-first algorithm and logarithmic quantization, the sufficient conditions for the bipartite synchronization of the addressed network are given by using Lyapunov method, inequality technique and Green’s formula. In addition, using M-matrix theory, the more applicable bipartite synchronization criteria in the form of low-dimensional linear matrix inequality and the form of network coupling strength threshold are given respectively. This work enriches and improves the previous works. At last, simulation experiments are offered to verify the correctness of our theoretical results.

Analysis and control for synchronization of coupled reaction–diffusion neural networks with multiple couplings subject to topology attacks

This paper addresses the synchronization for coupled reaction–diffusion neural networks (CRNNs) with multistate couplings or multiple spatial-diffusion couplings suffering topology attacks. By selecting appropriate Lyapunov functional and utilizing the Kronecker product, several network synchronization criteria are formulated. Moreover, since networks suffering attacks may not be synchronized in some circumstances, two simple controllers are also developed. Finally, the effectiveness of the devised control schemes are verified through two numerical examples.

Adaptive pinning cluster synchronization of a stochastic reaction–diffusion complex network

This work aims to achieve cluster synchronization of a complex network by some pinning control strategies. Firstly, the network not only is affected by the reaction–diffusion and the directed coupling phenomena, but also is disturbed by the stochastic noise and Markovian switching. Secondly, switched constant gain pinning, centralized and decentralized adaptive pinning are proposed respectively to realize the cluster synchronization of the considered network. In these adaptive pinning controllers, the control gain and coupling strength can been adjusted automatically while only a part of the nodes are controlled. Thirdly, the target state of cluster synchronization is taken as the average state related to the directed topology of all nodes in the same cluster, and does not need to be given separately as an isolated node. Finally, to verify the theoretical results, some simulations of directed coupled reaction–diffusion neural networks with stochastic noise and Markovian switching are given.

Quasi-synchronization of heterogeneous stochastic coupled reaction-diffusion neural networks with mixed time-varying delays via boundary control

In this paper, the quasi-synchronization problem of heterogeneous stochastic coupled neural networks (HSCNNs) is discussed. The effects of the mixed time-varying delay and diffusion phenomenon on the system are considered separately in time and space. Moreover, different from the previous distributed control, boundary control is introduced to realize network synchronization. This not only reduces the space cost of the controller, but also makes it easier to implement. Thus, the mean-square quasi-synchronization of HSCNNs is guaranteed by using matrix inequality and stochastic analysis tools. In addition to focusing on systems with Neumann boundary conditions, we briefly investigate HSCNNs with time-invariant delays and mixed boundary conditions respectively, and provide sufficient conditions to achieve the desired performance. Finally, the correctness of the conclusion is verified by several examples.

Delay-dependent passivity of impulsive coupled reaction–diffusion neural networks with multi-proportional delays

This article deals with passivity of coupled reaction–diffusion neural networks (CRDNNs) with multi-proportional delays and impulses. Two aspects are mainly considered: one is that the coupling term of the system depends on the delay, and the other is that the coupling term of the system is delay-independent. In order to simplify the complex system, the Kronecker product and its properties are applied to rewrite the complex system. According to whether the transfer function is a multi-proportional delayed function or a single proportional delayed function, several seemly Lyapunov Krasovskii functionals (LKFs) are constructed. Then, through the use of Kronecker product, Green’s formula and inequality analysis method, several criteria of input-strictly passivity (ISP) and output-strictly passivity (OSP) of the studied systems are attained, which all rely on proportional delayed factors. In addition, these criteria are exhibited in the form of matrix inequalities and can be checked with conventional software. Eventually, the passivity criteria are validated by two numerical examples and simulations.

Synchronization of fractional-order delayed neural networks with reaction–diffusion terms: Distributed delayed impulsive control

In this study, a new fractional Halanay-like impulsive differential inequality, which considers the system delay and impulse delay, is proposed for the first time. And accordingly, the quasi-synchronization problem of delayed fractional-order coupled reaction–diffusion neural networks (CRDNNs) is investigated. It is important to know that there are still relatively few studies on the impulsive synchronization control of fractional-order systems with time delay, and this study is an effective complement to this relevant field. To achieve quasi-synchronization, the distributed delayed impulsive control strategy is applied, which utilizes the local state information and the weighted average delayed information of other available neurons. Then, based on Wirtinger inequality, Lyapunov stability theory, and the properties of Mittag-Leffler function, some quasi-synchronization criteria are derived by solving some linear matrix inequalities (LMIs). Finally, a numerical simulation is provided to demonstrate the effectiveness of theoretical results, and reveal the effects of impulse delay and fractional order on the system synchronization rate.

Global Mittag-Leffler Stability of the Delayed Fractional-Coupled Reaction-Diffusion System on Networks Without Strong Connectedness.

In this article, we mainly consider the existence of solutions and global Mittag-Leffler stability of delayed fractional-order coupled reaction-diffusion neural networks without strong connectedness. Using the Leary-Schauder's fixed point theorem and the Lyapunov method, some criteria for the existence of solutions and global Mittag-Leffler stability are given. Finally, the correctness of the theory is verified by a numerical example.

Lag [formula omitted] synchronization in coupled reaction–diffusion neural networks with multiple state or derivative couplings

This paper mainly attempts to discuss lag H∞ synchronization in multiple state or derivative coupled reaction–diffusion neural networks without and with parameter uncertainties. Firstly, we respectively propose two types of reaction–diffusion neural networks with multiple state and derivative couplings subject to parameter uncertainties. Secondly, by exploiting designed state feedback controllers, several criteria of the lag H∞ synchronization for these two networks are developed based on Lyapunov functional and inequality techniques. Thirdly, lag H∞ synchronization issues of these two networks are also coped with by virtue of devised adaptive control strategies. Finally, we provide two numerical examples to verify the obtained lag H∞ synchronization criteria.

Synchronization for multiweighted and directly coupled reaction-diffusion neural networks with hybrid coupling via boundary control

This paper deals with the synchronization issue of multiweighted and directed coupled reaction-diffusion neural networks with hybrid coupling (MDCRDNNHC) based on boundary control. Spatial information is used for synchronization accompanied by state information, which is called hybrid coupling. By constructing appropriate controllers located in the boundary, synchronization matter for MDCRDNNHC with nonzero boundary values is solved. Inner coupling matrices (IMs) and outer coupling matrices (OMs) can be directed, competitive and even not connected in this paper. We propose a novel strategy to fuse current two technical routes for directed networks with multiweights. For MDCRDNNHC with diagonal IMs, we prove that if the weighted (added) combinations of multiple OMs for each dimension are strongly connected, and the Chebyshev distance among their normalized left eigenvectors of added OMs corresponding to zero eigenvalue for each dimension is less than a threshold, then synchronization can be attained. In addition, it is also applicable for positive definite but non-diagonal IMs under this fusion technique. Numerical examples are finally provided to demonstrate the effectiveness of these theoretical results.

Synchronization of Coupled Stochastic Reaction-Diffusion Neural Networks With Multiple Weights and Delays via Pinning Impulsive Control

The paper mainly investigates the synchronization problem of coupled stochastic reaction-diffusion neural networks with multiple weights and time delays via pinning impulsive control. Based on stochastic analysis theory, inequality technology, LMIs, and the principle of comparison, the sufficient conditions are obtained to ensure the synchronization of the coupled RDNNs with multiple weights and delays using a suitable pinning impulsive control protocol. Compared with the recent relevant theoretical research, the model established in this paper is more universal, and takes more industrial constraints into consideration. In addition, the synchronization criterion obtained in the paper has less restrictions. Finally, a numerical simulation is given to verify the correctness and feasibility of the theoretical results.

Synchronization and control for directly coupled reaction-diffusion neural networks with multiple weights and hybrid coupling

This article addresses the synchronization and pinning control problems of directly coupled reaction-diffusion neural networks (RDNNs). The model in this article has the following advantages: 1. the network can be directly coupled; 2. there are multiple coupling matrices to represent different communication channels; 3. the spatial information of RDNNs is also utilized for synchronization along with state information, which is called the hybrid coupling. Since different coupling matrices have different normalized left eigenvectors (NLEVec) corresponding to their zero eigenvalue, the design of Lyapunov functions, which heavily depends on NLEVec, will be prevented. In virtue of the weighted combination of NLEVec for multiple coupling matrices, we demonstrate that if the Chebyshev distance among these NLEVec is less than an allowable bound, then several synchronization and pinning control criteria with sufficiently large coupling strengths can be derived. In addition, the issue of adaptive coupling strengths is also addressed. Some numerical examples are finally simulated to illustrate the effectiveness of acquired results.

Event-triggered passivity and synchronization of coupled reaction–diffusion neural networks with and without time-varying delay

This paper is devoted to deal with the event-triggered passivity and synchronization problems for two types of coupled reaction–diffusion neural networks (CRDNNs). In the first type, several passivity and synchronization criteria for CRDNNs are acquired through designing suitable event-triggered controllers, combining some inequality techniques and Lyapunov functional approach. In the second type, the problems of event-triggered synchronization and passivity for coupled delayed reaction–diffusion neural networks (CDRDNNs) are investigated. Finally, two numerical examples are provided to illustrate the effectiveness of the derived passivity and synchronization conditions.