Invariant and attracting sets of Hopfield neural networks with delay

Abstract

This paper studies invariant and attracting sets of Hop® eld neural networks system with delay. SuYcient criteria are given for the invariant and attracting sets. In particular, we provide an estimate of the existence range of attractors by using invariant and attracting sets. Moreover, when the system has an equilibrium point, we obtain the suYcient conditions of global asymptotic stability of the equilibrium point. Several examples are also worked out to demonstrate the advantages of our results.

Attracting and invariant sets for a class of impulsive functional differential equations

“…According to the properties of M-matrix given in Definition 5, one can see that the above theorems are extension and improvement of the results on continuous dynamical systems in [17,18].…”

“…ential equations, partial differential equations and delay differential equations and so on [11][12][13][14][15][16][17][18]. Unfortunately, the corresponding problems for impulsive functional differential equations have not been considered prior to this work.…”

Bifurcation and Hybrid Control for A Simple Hopfield Neural Networks with Delays

“…. , ) varies, the sum of the orders of the zeros of (6) in the open right half-plane can change only if a zero appears on or crosses the imaginary axis.…”

“…Many stability criteria are obtained. We refer the reader to [1][2][3][4][5][6][7][8] and the references cited therein. However, the periodic nature of neural impulses is of fundamental significance in the control of regular dynamical functions such as breathing and heart beating.…”

Attracting and invariant sets of impulsive delay Cohen–Grossberg neural networks

“…Correspondingly, by using the linear inequality technique, a number of interesting results on the asymptotic behavior for differential systems have been reported; see Refs. [19][20][21][22]. However, the linear differential inequalities are ineffective for studying the asymptotic behavior of some nonlinear differential equations, such as system (1).…”