Shun-Yan Ren

Passivity analysis of impulsive coupled reaction-diffusion neural networks with and without time-varying delay

In this paper, we respectively investigate the input strict passivity and output strict passivity of impulsive coupled reaction-diffusion neural networks with and without time-varying delay. By constructing suitable Lyapunov functionals and utilizing some inequality techniques, several input strict passivity and output strict passivity conditions are derived for the impulsive coupled reaction-diffusion neural networks with and without time-varying delay. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the proposed results.

Passivity of linearly coupled neural networks with reaction–diffusion terms and switching topology

Abstract In this paper, we first propose a general array model of coupled reaction–diffusion neural networks with switching topology. Then, by utilizing the Lyapunov functional method combined with some inequality techniques, several sufficient conditions are established to ensure the input strict passivity and output strict passivity of the proposed network model. Furthermore, we reveal the relationship between passivity and stability of the proposed model. Based on the obtained passivity results and relationship between passivity and stability, a synchronization criterion is presented. Finally, two numerical examples are provided to demonstrate the correctness and effectiveness of the theoretical results.

Passivity of linearly coupled reaction-diffusion neural networks with switching topology and time-varying delay

This paper studies the passivity of a general array model of coupled reaction-diffusion neural networks (CRDNNs) with switching topology and time-varying delay. By exploiting the Lyapunov functional method and some inequality techniques, several sufficient criteria are established to ensure the input strict passivity and output strict passivity of the proposed network model. Moreover, we reveal the relationship between passivity and stability of CRDNNs. Based on the obtained passivity results and relationship between passivity and stability, a synchronization criterion is presented for CRDNNs. Finally, two numerical examples are provided to demonstrate the correctness and effectiveness of the theoretical results.

Impulsive control for the synchronization of coupled neural networks with reaction-diffusion terms

The impulsive control method is utilized to achieve the synchronization of coupled reaction-diffusion neural networks with time-varying delay. By combining the Lyapunov functional method with the impulsive delay differential inequality and comparison principle, a few sufficient conditions are derived to guarantee the global exponential synchronization of coupled neural networks with reaction-diffusion terms. Especially, the estimate for the exponential convergence rate is also given, which relies on time delay, system parameters and impulsive interval. Finally, numerical examples are provided to demonstrate the correctness and effectiveness of our results.

Passivity and Pinning Passivity of Coupled Delayed Reaction---Diffusion Neural Networks with Dirichlet Boundary Conditions

This paper respectively considers passivity problem and pinning passivity problem for coupled delayed reaction–diffusion neural networks (CDRDNNs). By construction of appropriate Lyapunov functionals and utilization of inequality techniques, several passivity conditions are derived for the CDRDNNs. Moreover, the pinning control technique is developed to obtain some passivity criteria for CDRDNNs. Finally, two numerical examples are also provided to verify the correctness of the theoretical results.

Passivity and pinning passivity of complex dynamical networks with spatial diffusion coupling

Abstract A coupled delayed reaction–diffusion neural networks (CDRDNNs) with spatial diffusion coupling is presented in this paper. By exploiting Lyapunov functional method as an effective tool, several passivity criteria for CDRDNNs with spatial diffusion coupling are established. Furthermore, pinning passivity of the CDRDNNs with spatial diffusion coupling has been deeply investigated and the corresponding conditions ensuring passivity of the CDRDNNs with spatial diffusion coupling are established. Two examples with simulation results are also given to verify the correctness of proposed passivity results.

Synchronization and H∞ synchronization of multi-weighted complex delayed dynamical networks with fixed and switching topologies

Abstract The synchronization and H ∞ synchronization of multi-weighted complex dynamical networks with fixed and switching topologies are respectively investigated in this paper. Firstly, by putting to use Lyapunov functional approach and some inequality techniques, we establish a synchronization criterion for the multi-weighted complex dynamical network with fixed topology. Moreover, the similar methods can be applied to get the criterion for achieving synchronization on multi-weighted complex dynamical networks with switching topology. In addition, when the above mentioned networks appear external disturbances, two criteria are acquired to ensure the H ∞ synchronization for the networks. Finally, two numerical examples are provided to demonstrate the correctness of the acquired synchronization criteria.

Pinning exponential synchronization and passivity of coupled delayed reaction-diffusion neural networks with and without parametric uncertainties

ABSTRACT In this paper, we focus on the pinning exponential synchronisation and passivity of coupled reaction–diffusion neural networks (CRDNNs) with and without parametric uncertainties, respectively. On the one hand, with the help of designed nonlinear pinning controllers and Lyapunov functional method, sufficient conditions are established to let the CRDNNs with hybrid coupling and mixed time-varying delays realise exponential synchronisation and passivity. On the other hand, considering that the external perturbations may lead the reaction–diffusion neural networks (RDNNs) parameters to containing uncertainties, the robust pinning exponential synchronisation and robust pinning passivity for coupled delayed RDNNs with parametric uncertainties are investigated by designing appropriate pinning control strategies. Finally, the effectiveness of the theoretical results are substantiated by the two given numerical examples.

Synchronization and Robust Synchronization for Fractional-Order Coupled Neural Networks

Synchronization and robust synchronization of fractional-order coupled neural networks (FCNNs) are considered in this paper. Different with the most published works on synchronization based on a special solution of an isolate node of the networks, we remove this restriction and introduce a more widely accepted definition of synchronization. Meanwhile, because of parametric uncertainties of network models, robust synchronization for FCNNs is investigated. In addition, by utilizing pinning control strategies, several sufficient conditions are derived to make sure that the considered networks can realize pinning synchronization and robust pinning synchronization. Finally, the correctness of the obtained results is substantiated by two given numerical examples.

Global exponential synchronization of nonlinearly coupled reaction-diffusion neural networks

This paper investigates the synchronization problem of nonlinearly coupled reaction-diffusion neural networks (NCRDNNs). By utilizing Lyapunov functional combined with several inequality techniques, a criterion for synchronization of NCRDNNs is presented. With designed pinning scheme, the synchronization problem of NCRDNNs is further discussed and a sufficient condition for pinning synchronization is also established. Finally, two numerical examples are given to verify the correctness and effectiveness of the theoretical results.