Bogdanov-Takens bifurcation in predator-prey systems

Bing Zeng; Shengfu Deng; Pei Yu

doi:10.3934/dcdss.2020130

Article Contents

2020, Volume 13, Issue 11: 3253-3269. Doi: 10.3934/dcdss.2020130

This issue Previous Article How interest rate influences a business cycle model Next Article Point to point traveling wave and periodic traveling wave induced by Hopf bifurcation for a diffusive predator-prey system

Bogdanov-Takens bifurcation in predator-prey systems

a.
School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, Guandong 524048, China
b.
Department of Applied Mathematics, Western University, London, Ontario, N6A 5B7, Canada
c.
School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China

^* Corresponding author: Pei Yu
^* Corresponding author: Pei Yu

Received: November 2018

Revised: February 2019

Early access: November 2019

Published: July 2020

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Abstract

In this paper, we consider Bogdanov-Takens bifurcation in two predator-prey systems. It is shown that in the full parameter space, Bogdanov-Talens bifurcation can be codimension $ 2 $, $ 3 $ or $ 4 $. First, the simplest normal form theory is applied to determine the codimension of the systems as well as the unfolding terms. Then, bifurcation analysis is carried out to describe the dynamical behaviour and bifurcation property of the systems around the critical point.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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