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Four Limit Cycles in Three-Dimensional Competitive Lotka-Volterra Systems of Class 28 in Zeeman's Classification

Mingzhi Hu, Zhengyi Lu, Yong Luo

Abstract

In this paper, a three-dimensional competitive Lotka-Volterra system with four limit cycles is constructed for class 28 in Zeeman's classification. Combined with existing results -- from Gyllenberg and Yan (2009) for class 27, from Wang, Huang and Wu (2011) for class 29, and from Yu, Han and Xiao (2016) for class 26 -- our finding indicates that there exist systems with at least four limit cycles for each class among classes 26 $-$ 29.

Four Limit Cycles in Three-Dimensional Competitive Lotka-Volterra Systems of Class 28 in Zeeman's Classification

Abstract

In this paper, a three-dimensional competitive Lotka-Volterra system with four limit cycles is constructed for class 28 in Zeeman's classification. Combined with existing results -- from Gyllenberg and Yan (2009) for class 27, from Wang, Huang and Wu (2011) for class 29, and from Yu, Han and Xiao (2016) for class 26 -- our finding indicates that there exist systems with at least four limit cycles for each class among classes 26 29.

Paper Structure

This paper contains 4 sections, 11 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Automated search algorithm
  3. Four limit cycles in class 28
  4. Concluding remarks