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Dynamical Behaviors of a Large Class of General Delayed Neural Networks

tchen{at}fudan.edu.cn, Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai, 200433, China

Wenlian Lu

chiquitita{at}21cn.com, Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai, 200433, China

Guanrong Chen

gchen{at}ee.cityu.edu.hk, Electronic Engineering Department, City University of Hong Kong, Kowloon, Hong Kong, China

Research of delayed neural networks with varying self-inhibitions, interconnection weights, and inputs is an important issue. In the real world, self-inhibitions, interconnection weights, and inputs should vary as time varies. In this letter, we discuss a large class of delayed neural networks with periodic inhibitions, interconnection weights, and inputs. We prove that if the activation functions are of Lipschitz type and some set of inequalities, for example, the set of inequalities 3.1 in theorem 1, is satisfied, the delayed system has a unique periodic solution, and any solution will converge to this periodic solution. We also prove that if either set of inequalities 3.20 in theorem 2 or 3.23 in theorem 3 is satisfied, then the system is exponentially stable globally. This class of delayed dynamical systems provides a general framework for many delayed dynamical systems. As special cases, it includes delayed Hopfield neural networks and cellular neural networks as well as distributed delayed neural networks with periodic self-inhibitions, interconnection weights, and inputs. Moreover, the entire discussion applies to delayed systems with constant self-inhibitions, interconnection weights, and inputs.

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