S1 attractor bifurcation analysis for a three-species cooperating model

In this paper, the dynamic bifurcation of the three-species cooperating model is considered. It worth noting that the main theory of this paper is the Center manifold reduction and attractor bifurcation theory, which is developed by Ma [1,2]. The main work of this paper shows that if the algebraic m...

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Bibliographic Details
Published in:Journal of physics. Conference series Vol. 2282; no. 1; pp. 012014 - 12020
Main Authors: Li, Junyan, Wu, Ruili
Format: Journal Article
Language:English
Published: Bristol IOP Publishing 01.06.2022
Subjects:
Bifurcation theory
Eigenvalues
Physics
ISSN:1742-6588, 1742-6596
Online Access:Get full text
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Summary:In this paper, the dynamic bifurcation of the three-species cooperating model is considered. It worth noting that the main theory of this paper is the Center manifold reduction and attractor bifurcation theory, which is developed by Ma [1,2]. The main work of this paper shows that if the algebraic multiplicity of the first eigenvalue is 2, there exists an S1 attractor bifurcation, and the number of its singular points can only be eight. Besides, we show that the simplified governing equations bifurcate to an S1 attractor, when the Control parameter λ crosses a critical value λ0.
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ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/2282/1/012014