Abstract
In this paper, we consider a class of Cohen-Grossberg neural networks with mixed delays. Different from the previous literature, we study the existence and exponential stability of pseudo almost automorphic solutions for the suggested system. Our method is mainly based on the Banach fixed point theorem and the Lyapunov functional method. Moreover, a numerical example is given to show the effectiveness of the main results.
Highlights
The concept of pseudo almost automorphy was first introduced by Xiao et al [ ], which is a natural generalization of almost periodicity and almost automorphy
Motivated by the above discussion, in this paper we study the existence, uniqueness, and exponential stability of pseudo almost automorphic solutions for the following Cohen-Grossberg neural networks (CGNNs):
By using the Banach fixed point theorem and the Lyapunov functional method, we prove the existence, uniqueness, and exponential stability of pseudo almost automorphic solutions to system ( )
Summary
The concept of pseudo almost automorphy was first introduced by Xiao et al [ ], which is a natural generalization of almost periodicity and almost automorphy. Motivated by the above discussion, in this paper we study the existence, uniqueness, and exponential stability of pseudo almost automorphic solutions for the following CGNNs:. By using the Banach fixed point theorem and the Lyapunov functional method, we prove the existence, uniqueness, and exponential stability of pseudo almost automorphic solutions to system ( ). [ ] A continuous function f : R × Rm → Rm is said to be almost automorphic if for every sequence of (sn)n∈N , there exists a subsequence (sn)n∈N ⊂ (sn)n∈N such that g (t, x) sn, x) is well defined for each t ∈ R, x ∈ Rm, and lim n→∞. = f ∈ BC R × Rm, Rm lim f (t, x) dt = , ∀x ∈ Rm , where BC(R, Rm) (or BC(R × Rm, Rm)) is the collection of the set of bounded continuous functions from R (or R × Rm) to Rm. Definition .
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