Dynamics of solution for a class of delayed diffusive neural networks with mixed boundary conditions

Authors:
Jianghong Bai;Zhidong Teng;Haijun Jiang
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, People's Republic of China;College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, People's Republic of China;College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, People's Republic of China
Venue:
Neurocomputing
Year:
2010

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Abstract

In this paper, we investigate a class of cellular neural networks model with delays and diffusive terms. By using the method of upper and lower solutions, we obtain that if the neuronal output signal functions in system possess mixed quasimonotone property and the corresponding elliptic system has upper and lower solutions the model has a unique nonconstant equilibrium solution. Under some additional conditions we further obtain that the solution of the neural networks converges to this nonconstant equilibrium solution.