Global attractivity and existence of weighted pseudo almost automorphic solution for GHNNS with delays and variable coefficients

Abstract

In this paper, we shall explain a new result concerning weighted pseudo almost automorphic solutions of Hopfield neural network with time-varying delay and variable coefficients. Precisely, we shall prove existence and the global attractivity of the unique weighted pseudo almost automorphic solution of the considered model. Then, by employing suitable analytic techniques, global attractivity of the unique weighted pseudo almost automorphic solution is established. Lastly, an example is provided to demonstrate the validity of the results proposed.

Pseudo almost automorphic solutions to non autonomous third order differential equation with multiple deviating arguments

“…In [24], Xiao et al introduced a new class of functions, which is the pseudo almost automorphic and which is the most important generalization of the almost automorphic functions. These functions were used in many fields, and are the most attractive topics in the qualitative theory of differential equations because of their significance and applications in physics, mathematical biology, control theory, and other related fields ( one can see [4,11,12,13,21]).…”