# American Institute of Mathematical Sciences

November  2020, 13(11): 3253-3269. doi: 10.3934/dcdss.2020130

## 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

Received  November 2018 Revised  February 2019 Published  November 2019

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.

Citation: Bing Zeng, Shengfu Deng, Pei Yu. Bogdanov-Takens bifurcation in predator-prey systems. Discrete & Continuous Dynamical Systems - S, 2020, 13 (11) : 3253-3269. doi: 10.3934/dcdss.2020130
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