Impulsive Hopfield-type neural network system with piecewise constant argument


AKHMET M. , YILMAZ E.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, vol.11, no.4, pp.2584-2593, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.1016/j.nonrwa.2009.09.003
  • Title of Journal : NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
  • Page Numbers: pp.2584-2593
  • Keywords: Impulsive differential equations, Hopfield neural networks, Piecewise constant argument, Equilibrium, Asymptotic stability, Periodic solutions, DIFFERENTIAL-EQUATIONS, GENERALIZED TYPE, STABILITY, OSCILLATORS

Abstract

In this paper we introduce an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Sufficient conditions for the existence of the unique equilibrium are obtained. Existence and uniqueness of solutions of such systems are established. Stability criterion based on linear approximation is proposed. Some sufficient conditions for the existence and stability of periodic solutions are derived. An example with numerical simulations is given to illustrate our results. (C) 2009 Elsevier Ltd. All rights reserved.