Abstract
This paper investigates global synchronization in an array of coupled neural networks with time-varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a novel integral inequality and the Lyapunov functional method, sufficient synchronization criteria are derived. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using Matlab LMI Toolbox. It is displayed that, when some of the transmission efficiencies are limited, the dynamics of the synchronized state are different from those of the isolated node. Furthermore, the transmission efficiency and inner coupling matrices between nodes play important roles in the final synchronized state. The derivative of the time-varying delay can be any given value, and the time-varying delay can be unbounded. The outer-coupling matrices can be symmetric or asymmetric. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.
Highlights
In the past few decades, the problem of chaos synchronization and network synchronization has been extensively studied since its potential engineering applications such as communication, biological systems, and information processing
Motivated by the above analysis, this paper studies the synchronization in an array neural network with both timevarying delays and unbounded distributed delays, under the condition that the transmission efficiencies among nodes are limited
Synchronization criteria in an array of coupled neural networks with limited transmission efficiency are obtained in Theorem and Corollary
Summary
In the past few decades, the problem of chaos synchronization and network synchronization has been extensively studied since its potential engineering applications such as communication, biological systems, and information processing (see [1,2,3,4] and the references therein). Note that most existing results on stability or synchronization of neural networks with bounded distributed delays obtained by using LMI approach cannot be directly extended to those with unbounded distributed delays. There were some results on stability or synchronization of neural networks with unbounded distributed delays, some of them were obtained by using algebra approach [27,28,29,30]. In this paper we investigate the synchronization in an array of coupled neural networks with both discrete time-varying delays and unbounded distributed delays based on LMI approach. Results of the present paper are applicable to synchronization of complex networks with bounded or unbounded distributed time delay. Motivated by the above analysis, this paper studies the synchronization in an array neural network with both timevarying delays and unbounded distributed delays, under the condition that the transmission efficiencies among nodes are limited. A > 0 or A < 0 denotes that the matrix A is a symmetric and positive or negative definite matrix
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