Year: 2021
Author: Qinlong Wang, Jingping Lu, Wentao Huang, Bo Sang
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 1 : pp. 1–12
Abstract
The main objective of this paper is not only to find necessary and sufficient conditions for the existence of a center on a local center manifold for a three dimensional Lotka-Volterra system, but also to determine the maximum number of limit cycles that can bifurcate from the positive equilibrium as a fine focus. Firstly, the singular point quantities are computed and simplified to obtain necessary conditions for local integrability, and Darboux method is applied to show the sufficiency. Then, the Hopf bifurcation on the center manifold is investigated, from this, the conclusion of at most five small limit cycles generated in the vicinity of the equilibrium is obtained. To the best of our knowledge, this is the first case with five possible limit cycles for the cyclicity of 3D Lotka-Volterra systems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2021.1
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 1 : pp. 1–12
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: 3D Lotka-Volterra system Hopf bifurcation Center problem Singular point quantities.