Yan-Li Huang

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.

Analysis and pinning control for passivity of coupled reaction-diffusion neural networks with nonlinear coupling

Abstract 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.

Pinning synchronization of spatial diffusion coupled reaction-diffusion neural networks with and without multiple time-varying delays

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.

Finite-time synchronization of multi-weighted complex dynamical networks with and without coupling delay

Abstract Two kinds of multi-weighted complex dynamical networks models with and without coupling delay are respectively considered in this paper. First of all, a finite-time synchronization criterion which ensures that multi-weighted complex dynamical networks with fixed topology and constant coupling realize synchronization in finite time is established by means of Lyapunov functional and state feedback controllers. On the basis of Dini derivative and some inequality techniques, a sufficient condition which guarantees synchronization in finite time of multi-weighted complex dynamical networks with switching topology and constant coupling is acquired. On the other hand, in view of the research results above, we similarly investigate multi-weighted complex dynamical networks with time delayed coupling. Two numerical examples finally are provided to verify the availability of the proposed results.

Pinning synchronization of complex dynamical networks with and without time-varying delay

Abstract 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.

Passivity and synchronization of coupled reaction–diffusion Cohen–Grossberg neural networks with state coupling and spatial diffusion coupling

Abstract This paper deals with the passivity and synchronization problems for two types of coupled reaction–diffusion Cohen–Grossberg neural networks (CRDCGNNs). On the one side, a CRDCGNNs model with state coupling is introduced, and several sufficient conditions which ensure the passivity and synchronization of this type of network are deduced respectively by resorting to some inequality techniques and Lyapunov functional method. On the other side, considering that the different diffusion of each node may give rise to different changes of other nodes in reaction–diffusion networks, we also carry out some investigations on the passivity and synchronization of CRDCGNNs with spatial diffusion coupling. Finally, the correctness of the obtained research results are corroborated by two illustrative examples.

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.