Existence of generalized homoclinic solutions of lotka-volterra system under a small perturbation

This paper investigates lotka-volterra system under a small perturbation vxx = - μ (1-a2u-v) v+ϵ f (ϵ,v,vx,u,ux),uxx = - (1-u-a1 v) u+ϵg (ϵ,v,vx,u,ux). 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. © 2016 yuzhen mi.