Special Session 146: Nonlinear differential equations: control, delay, and boundary value problems

Convergence of asymptotic systems in Cohen-Grossberg neural network models with unbounded delays
Jos\`{e} J. Oliveira
University of Minho
Portugal
Co-Author(s):    A. Elmwafy, Jos\\`e J. Oliveira, and C\\`esar M. Silva
Abstract:
In this presentation, we present sufficient conditions for the convergence of asymptotic systems in non-autonomous Cohen-Grossberg neural network models that incorporate both infinite discrete time-varying and distributed delays. The main stability criterion is obtained by imposing conditions under which the non-delay terms asymptotically dominate the delay terms. As an applications, we provide sufficient conditions ensuring that all solutions of a non-periodic neural network model with unbounded delays converge to a periodic function as time goes to infinity. A numerical example is presented to illustrate the effectiveness of the new results.