Rough center in a 3-dimensional Lotka-Volterra system
type: Item
instance of: scholarly article
title: Rough center in a 3-dimensional Lotka-Volterra system
zbMATH Open document ID: 1441.37102
DOI: 10.1504/IJDSDE.2020.106026
author: Yusen Wu
author: Laigang Guo
published in: International Journal of Dynamical Systems and Differential Equations
publication date: 2020-04-07T00:00:00Z
review text: Summary: This paper identifies rough center for a Lotka-Volterra system, a 3-dimensional quadratic polynomial differential system with four parameters \(h\), \(n\), \(\lambda\), \(\mu\). The known work shows the appearance of four limit cycles, but centre condition is not determined. In this paper, we verify the existence of at least four limit cycles in the positive equilibrium due to Hopf bifurcation by computing normal forms. Furthermore, by applying algorithms of computational commutative algebra we find Darboux polynomial and give a centre manifold in closed form globally, showing that the positive equilibrium of centre-focus is actually a rough center on a centre manifold.
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34C07
zbMATH DE Number: 7186976
zbMATH Keywords: rough center
zbMATH Keywords: 3-dimensional Lotka-Volterra system
zbMATH Keywords: normal form theory
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 7186976