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This paper presents a general array model of switched coupled reaction–diffusion neural networks (CRDNNs) with non-delayed and delayed couplings. By utilizing some inequality techniques, we derive several sufficient conditions ensuring the input strict passivity and output strict passivity of the proposed network model. In addition, by constructing an appropriate Lyapunov functional, a sufficient condition is established in the form of linear matrix inequations to guarantee synchronization of CRDNNs with switched topology. Numerical examples with simulation results are provided to demonstrate the effectiveness and correctness of the obtained results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of two kinds of coupled neural networks with different dimensions for input and output vectors, that is, the case with and without time-varying delay. On one side, we analyse the passivity of these coupled neural networks by employing some inequality techniques and a Lyapunov functional approach. On the other side, by designing appropriate pinning control schemes, several conditions are derived, which can make sure that the considered networks are passivity. Finally, numerical examples are given to confirm the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper addresses the passivity and passivity-based synchronization problems of an array model of nonlinearly coupled neural networks (NCNNs) with reaction-diffusion terms. Several sufficient conditions are established to guarantee the passivity of the considered network model by exploiting the Lyapunov functional method and some inequality techniques. Additionally, pinning control is an efficient technique for the investigation of passivity of complex networks. Because of this, the passivity of the proposed model is further studied by designing suitable pinning controller, and some pinning passivity criteria are also presented. On the other hand, the relationship between stability and (pinning) passivity is also analyzed. Several criteria for (pinning) synchronization are established by taking advantage of the relationship between exponential stability and (pinning) passivity. In the last, we provide two examples to elucidate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, two coupled reaction-diffusion neural networks (CRDNNs) with spatial diffusion coupling are studied. In the first one, the single reaction-diffusion neural network (RDNN) is coupled by their current states. The single RDNN is coupled by their current states and delayed states in the second one. Combined with some inequality techniques and Lyapunov functional approach, a synchronization criterion for the first network model is established via adding controllers to the first l nodes. In addition, a sufficient condition is derived to make sure that the considered network can achieve synchronization by designing pinning adaptive feedback controllers. Similarly, the pinning synchronization for the second network model is also considered. Finally, the correctness of the obtained results are confirmed by numerical simulation in two illustrated examples. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we respectively discuss passivity and pinning passivity of multi-weighted complex dynamical networks. By employing Lyapunov functional approach, several passivity criteria for the complex dynamical network with fixed topology and multi-weights are established. In addition, under the designed pinning adaptive state feedback controller, some sufficient conditions are obtained to ensure the passivity of the multi-weighted complex dynamical network with fixed topology. Furthermore, similar methods are used to derive several criteria for passivity and pinning passivity of complex dynamical networks with switching topology and multi-weights. Finally, two numerical examples with simulation results are given to show the correctness of the obtained passivity criteria. [ABSTRACT FROM AUTHOR]

The pinning synchronization in two types of complex dynamical networks are studied in this paper. In the first one, the nodes are coupled by their states; In the second one, the nodes are coupled by their past states or delayed states. By designing suitable pinning control schemes, several synchronization criteria are derived for these proposed network models. Moreover, some adaptive strategies are developed to get proper coupling strength for the first network model. For the second network model, we give several synchronization criteria by utilizing the designed pinning adaptive feedback controllers. Finally, two numerical examples indicate that complex dynamical networks with and without time-varying delay can achieve synchronization by pinning a small fraction of nodes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]