On the role of diffusion factors in stability analysis for p-Laplace dynamical equations involved to BAM Cohen-Grossberg neural network

• Published in: Neurocomputing (Amsterdam) Vol. 223; pp. 54 - 62
• Main Authors: Rao, Ruofeng, Zhong, Shouming, Pu, Zhilin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 05.02.2017
• Subjects: Fuzzy BAM Cohen-Grossberg neural network; M-matrix; Nonlinear diffusion; Reaction-diffusion; Variational methods; M-matrix; Variational methods; Nonlinear diffusion; Reaction-diffusion; Fuzzy BAM Cohen-Grossberg neural network
• ISSN: 0925-2312; 1872-8286
• DOI: 10.1016/j.neucom.2016.10.036

In the ordinary differential system, the uniqueness of its equilibrium point can be determined obviously by the global asymptotic stability of this point. However, the reaction-diffusion dynamical system is partial differential equations with respect to both time variable t and space variable x so that the uniqueness of its equilibrium point need to be proved solely. In this paper, a comprehensive application of M-Matrix technique, Lyapunov functional method, Yang inequality and variational methods demonstrates the unique existence of globally asymptotically stable trivial equilibrium solution for the fuzzy dynamical system with nonlinear p-Laplace (p>1) diffusion. Especially when p=2, it becomes the reaction-diffusion fuzzy BAM Cohen-Grossberg neural network (BAM CGNN). Or if diffusion phenomena are ignored, it degrades into the fuzzy ordinary differential BAM CGNN. Even in such a special case, the derived corollary is also novel against existing results due to not exerting the boundedness control on the amplification functions. Moreover, the effectiveness of the proposed methods is illustrated by a numerical example and a comparable table.