Linearization of Impulsive Differential Equations with Ordinary Dichotomy

Yongfei Gao, Xiaoqing Yuan, Yonghui Xia and P. J. Y. Wong

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: This paper presents a linearization theorem for the impulsive differential equations when the linear system has ordinary dichotomy. We prove that when the linear impulsive system has ordinary dichotomy, the nonlinear system x˙(t)=A(t)x(t)+f(t,x), t ≠ tk, Δx(tk)=A~(tk)x(tk)+f~(tk,x), k ∈ ℤ, is topologically conjugated to x˙(t)=A(t)x(t), t ≠ tk, Δx(tk)=A~(tk)x(tk), k ∈ ℤ, where Δx(tk)=x(tk+)-x(tk-), x(tk-)=x(tk), represents the jump of the solution x(t) at t = tk. Finally, two examples are given to show the feasibility of our results.

Date: 2014
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https://doi.org/10.1155/2014/632109

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:632109

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