Global Exponential Stability of Almost Periodic Solution for A Large Class of Delayed Dynamical Systems

TL;DR

This paper proves the global exponential stability of almost periodic solutions in a broad class of delayed dynamical systems with time-varying parameters, including neural networks with delays and variable coefficients.

Contribution

It introduces a new approach to establish the existence and stability of almost periodic solutions without relying on traditional methods.

Findings

Unique almost periodic solution exists under mild conditions.

The solution is globally exponentially stable.

Applicable to systems with time-varying delays and distributed delays.

Abstract

Research of delayed neural networks with variable self-inhibitions, inter-connection weights, and inputs is an important issue. %In the real world, self-inhibitions, %inter-connection weights, and inputs should vary through time. In In this paper, we discuss a large class of delayed dynamical systems with almost periodic self-inhibitions, inter-connection weights, and inputs. This model is universal and includes delayed systems with time-varying delays, distributed delays as well as combination of both. We prove that under some mild conditions, the system has a unique almost periodic solution, which is globally exponentially stable. We propose a new approach, which is independent of existing theory concerning with existence of almost periodic solution for dynamical systems.