Title: Rough center in a 3-dimensional Lotka-Volterra system

Authors: Yusen Wu; Laigang Guo

Addresses: School of Statistics, Qufu Normal University, Qufu, Shandong 273165, China ' School of Mathematical Science, University of Chinese Academy of Sciences, Beijing 100049, China

Abstract: This paper identifies rough center for a Lotka-Volterra system, a 3-dimensional quadratic polynomial differential system with four parameters h, n, λ, μ. 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.

Keywords: rough center; 3-dimensional Lotka-Volterra system; Normal form theory.

DOI: 10.1504/IJDSDE.2020.106026

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.2, pp.116 - 127

Received: 11 Apr 2018
Accepted: 10 Sep 2018
Published online: 25 Mar 2020 *

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