Existence of generalized homoclinic solutions of Lotka-Volterra system under a small perturbation
type: Item
instance of: scholarly article
title: Existence of generalized homoclinic solutions of Lotka-Volterra system under a small perturbation
zbMATH Open document ID: 1377.37034
DOI: 10.1155/2016/8075381
author: Yuzhen Mi
published in: Journal of Function Spaces
publication date: 2016-07-29T00:00:00Z
review text: The author considers the perturbed Lotka-Volterra system \[ v_{xx}=-\mu(1-a_2 u-v)v+\epsilon f(\epsilon,v,v_x,u,u_x),\;\;u_{xx}=-(1-u-a_1v)u+\epsilon g(\epsilon,v,v_x,u,u_x), \] for \(x\in \mathbb{R}\), with constants \(\mu>0\), \(a_1<1<a_2\), where \(f,g\) are smooth and \(\epsilon>0\) is a small parameter. Moreover, it is assumed that the functions \(f,g\) have certain reflection symmetries which yield a reversible system. For \(\mu\) sufficiently small, they establish the existence of a solution that is homoclinic to a small amplitude periodic orbit that emerges from a Hopf bifurcation.
reviewed by: Christos Sourdis
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 37G20
zbMATH DE Number: 6607728
zbMATH Keywords: Lotka-Volterra system
zbMATH Keywords: Fourier series expansion
zbMATH Keywords: fixed point theorem
zbMATH Keywords: homoclinic solution
Wikidata QID: Q59126543
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/8075381
OpenAlex ID: W2469734838
cites work: Q3238801
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description: scientific article; zbMATH DE number 6607728