Letters: On the almost periodic solution of generalized Hopfield neural networks with time-varying delays

Authors:
Yiguang Liu;Zhisheng You;Liping Cao
Affiliations:
Institute of Image & Graphics, School of Computer Science and Engineering, Sichuan University, Chengdu 610064, P. R. China and Center for Nonlinear and Complex Systems, School of Electronic Engine ...;Institute of Image & Graphics, School of Computer Science and Engineering, Sichuan University, Chengdu 610064, P. R. China;Sichuan University Library, Sichuan University. Chengdu 610054, P. R. China
Venue:
Neurocomputing
Year:
2006

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Abstract

This paper presents several sufficient conditions about existence, uniqueness and stability of the almost periodic solution of general Hopfield neural networks with time-varying delays using exponential dichotomy, several fixed point theorems, Halanay inequality, Lyapunov functional and some inequality techniques. These results extend and improve some known relevant works, e.g. the restrictions to the connection weight matrices are slacker, and it is not required that the activation functions are globally Lipschitzian. Most importantly, these conditions are easy to check and apply. Finally, one example is employed to illustrate the conclusions, and the simulated results show the validity. Particularly, the right assertion about the existence, uniqueness and stability of the almost periodic solution of the specific generalized Hopfield neural networks is given only by our criteria, and the relevant criteria provided by a recent reference fail.