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The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits

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  • Han Xu
  • Yinlai Jin

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.

Suggested Citation

  • Han Xu & Yinlai Jin, 2016. "The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-8, February.
    • Handle: RePEc:hin:jnddns:6405853
    DOI: 10.1155/2016/6405853
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