Event‐triggered pinning synchronization and robust pinning synchronization of coupled neural networks with multiple weights

Abstract

In this paper, we, respectively, solve the problems of event-triggered pinning synchronization and robust pinning synchronization of multiple weighted coupled neural networks (MWCNNs). By devising suitable event-triggered controller, some pinning synchronization and robust pinning synchronization criteria for MWCNNs with the appropriate event-triggered condition are deduced, respectively, on the basis of some inequalities and the theory of Lynapunov functional. Furthermore, we research the event-triggered pinning synchronization and event-triggered robust pinning synchronization of multiple weighted coupled delayed neural networks and establish some correlative synchronization criteria, respectively, on the basis of appropriate event-triggered condition and pinning controller. At last, the numerical simulation results in two examples verify the validity of the theoretical results.

Event‐triggered pinning control for passivity and synchronization of directly coupled delayed reaction‐diffusion neural networks

“…Remark 7. Lately, many scholars have paid much attention to dynamical behaviors of CNNs, and numerous passivity and synchronization results have been obtained, [32][33][34][35][36][37][38][39][40][41][42] and applied successfully to image encryption and secure communication. 32,33 Notice that RDP is neglected in previous works above, and models of CNNs are built based on a set of ordinary differential equations, which only depend on time variable for the nodes' state.…”

“…Reference 39 studied partially CNNs based on event‐triggered mechanism, and proposed several synchronization‐based passivity conditions. Until now, only few authors have considered the synchronization problem for CNNs by employing even‐triggered pinning control scheme 41,42 . Reference 42 discussed cluster synchronization matter for CNNs by exploiting event‐triggered pinning protocol and data sampling strategy.…”

“…We build a general model of directly CDRDNNs, where dimensions of input and output vectors are different. Compared with previously published literature, [34][35][36][37][38][39][40][41][42] the presented model includes reaction-diffusion term and time-varying delay, and with directly coupled in our article (i.e., directly CDRDNNs), which is more general and comprehensive, and can reveal more networks well in practice.…”

“…Until now, only few authors have considered the synchronization problem for CNNs by employing even-triggered pinning control scheme. 41,42 Reference 42 discussed cluster synchronization matter for CNNs by exploiting event-triggered pinning protocol and data sampling strategy.…”

“…However, most results established in previous related works, [29][30][31]41,42 ignore reaction-diffusion phenomenon (RDP). In practical situation, it is unavoidable for network systems to appear RDP, such as neural networks and social networks 43,44 when neural networks are implemented by electric circuits.…”