Four Limit Cycles in Three-Dimensional Competitive Lotka-Volterra Systems of Class 28 in Zeeman's Classification
Dynamical Systems
2026-03-27 v1
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.
Keywords
Cite
@article{arxiv.2603.24612,
title = {Four Limit Cycles in Three-Dimensional Competitive Lotka-Volterra Systems of Class 28 in Zeeman's Classification},
author = {Mingzhi Hu and Zhengyi Lu and Yong Luo},
journal= {arXiv preprint arXiv:2603.24612},
year = {2026}
}