Quasi-periodic solutions of the Lotka-Volterra competition systems with quasi-periodic perturbations
type: Item
instance of: scholarly article
title: Quasi-periodic solutions of the Lotka-Volterra competition systems with quasi-periodic perturbations
zbMATH Open document ID: 1251.37076
author: Qihuai Liu
author: Dingbian Qian
author: Zhiguo Wang
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2012-07-04T00:00:00Z
review text: The authors study an \(N\)-species Lotka-Volterra competition systems with quasi-periodic coefficients. Through constructing a Newton iteration they prove an abstract KAM theorem. Then they confirm the existence of positive quasi-periodic solutions for these LV systems. The result shows that, in most case, quasi-periodic solutions exist for sufficiently small quasi-periodic perturbations of the autonomous Lotka-Volterra systems. Moreover, these quasi-periodic solutions will tend to an equilibrium of the autonomous Lotka-Volterra systems.
reviewed by: Fengqin Zhang
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34C27
zbMATH DE Number: 6052995
zbMATH Keywords: Lotka-Volterra competition system
zbMATH Keywords: quasi-periodic solution
zbMATH Keywords: KAM iteration
zbMATH Keywords: small denominator
MaRDI profile type: Publication
full work available at URL: dcdsb.2012.17.1537
OpenAlex ID: W2062332962
DOI: 10.3934/DCDSB.2012.17.1537
description: scientific article; zbMATH DE number 6052995