Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation. (28th June 2016)

• Record Type: Journal Article
• Authors: Mi, Yuzhen
• Other Names: Leśniak Zbigniew Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-06-28
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/8075381
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper investigates Lotka-Volterra system under a small perturbation v x x = - μ ( 1 - a 2 u - v ) v + ϵ f ( ϵ, v, v x, u, u x ), u x x = - ( 1 - u - a 1 v ) u + ϵ g ( ϵ, v, v x, u, u x ) . By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ = 0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.