Linearization of Impulsive Differential Equations with Ordinary Dichotomy. (2nd March 2014)

• Record Type: Journal Article
• Authors: Gao, Yongfei; Yuan, Xiaoqing; Xia, Yonghui; Wong, P. J. Y.
• Other Names: Song Yongli Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-03-02
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/632109
• Languages: English
• ISSNs: 1085-3375

Abstract

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 ≠ t k, Δ x ( t k ) = A ~ ( t k ) x ( t k ) + f ~ ( t k, x ), k ∈ ℤ, is topologically conjugated to x ˙ ( t ) = A ( t ) x ( t ), t ≠ t k, Δ x ( t k ) = A ~ ( t k ) x ( t k ), k ∈ ℤ, where Δ x ( t k ) = x ( t k + ) - x ( t k - ), x ( t k - ) = x ( t k ), represents the jump of the solution x ( t ) at t = t k . Finally, two examples are given to show the feasibility of our results.