Stability for the mix-delayed Cohen-Grossberg neural networks with nonlinear impulse

Abstract

In this paper, the authors are concerned with the stability of the mix-delayed CohenGrossberg neural networks with nonlinear impulse by the nonsmooth analysis. Some novel sufficient conditions are obtained for the existence and the globally asymptotic stability of the unique equilibrium point, which include the well-known results on some impulsive systems and non-impulsive systems as its particular cases. The authores also analyze the globally exponential stability of the equilibrium point. Two examples are exploited to illustrate the feasibility and effectiveness of our results.

General stability for a Cohen–Grossberg neural network system

“…The fact that the equilibrium exists and is unique has been proved in [3,14,16,[18][19][20][21]23,24]. Theorem 2.2 Under the above assumptions, Problem (1) admits a unique equilibrium.…”

“…for some positive constant β (just as in the HNN case with distributed delays) in [3,14,16,[19][20][21]23,24]. There are many works on stability for similar problems, but without explicit decay.…”

Novel Criteria of ISS Analysis for Delayed Memristive Simplified Cohen–Grossberg BAM Neural Networks

“…erefore, stability problems have attracted many researchers'attentions [9][10][11][12][13][14][15][16]. Based on nonsmooth analysis and stability theory, we obtained sufficient conditions of the globally asymptotical stability of the mix-delayed Cohen-Grossberg neural networks with nonlinear impulse [13]. Considering characteristics of BAM neural networks and Cohen-Grossberg neural networks, many researchers investigated qualitative analysis of Cohen-Grossberg BAM neural networks [16][17][18].…”