Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation

Abstract EN

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.