Existence and Global Exponential Stability of Almost Periodic Solutions for a Class of Delay Duffing Equations on Time Scales

Abstract

Based on the exponential dichotomy of linear dynamic equations on time scales, we obtain some sufficient conditions for the existence and global exponential stability of almost periodic solutions for a class of Duffing equations with time-varying delays on time scales. We also present numerical examples to show the feasibility of obtained results. The results of this paper are completely new even when the time scale $\mathbb{T}=\mathbb{R}$ or $\mathbb{Z}$ and are complementary to the previously known results.