In this paper we mainly study the existence of periodic solutions for a system of delay differential equations representing a simple two-neuron network model of Hopfield type with time-delayed connections between the neurons. We first examine the local stability of the trivial solution, propose some sufficient conditions for the uniqueness of equilibria and then apply the Poincar?-Bendixson theorem for monotone cyclic feedback delayed systems to establish the existence of periodic solutions. In addition, a sufficient condition that ensures the trivial solution to be globally exponentially stable is also given. Numerical examples are provided to support the theoretical analysis. ? 2009 Elsevier Ltd. All rights reserved.
Relation:
Nonlinear Analysis, Theory, Methods and Applications Volume 71, Issue 12, 15 December 2009, Pages 6222-6231
