The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits. (4th February 2016)

• Record Type: Journal Article
• Authors: Xu, Han; Jin, Yinlai
• Other Names: Akın Elvan Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2016(2016)
• Publication Date: 2016-02-04
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2016/6405853
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : Singularly perturbed problems are often used as the models of ecology and epidemiology. In this paper, a class of semilinear singularly perturbed systems with contrast structures are discussed. Firstly, we verify the existence of heteroclinic orbits connecting two equilibrium points about the associated systems for contrast structures in the corresponding phase space. Secondly, the asymptotic solutions of the contrast structures by the method of boundary layer functions and smooth connection are constructed. Finally, the uniform validity of the asymptotic expansion is defined and the existence of the smooth solutions is proved.