Codimension two 1:1 strong resonance bifurcation in a discrete predator-prey model with Holling Ⅳ functional response

AIMS Mathematics

Mianjian Ruan¹  Xianyi Li¹  Chang Li² 

[1] 1. Department of Big Data Science, School of Science Zhejiang University of Science and Technology, Hangzhou 310023, China;2. Shenzhen Experimental School, Shenzhen 518028, China;

关键词: predator-prey model;    holling ⅳ functional response;    transcritical bifurcation;    1:1 strong resonance bifurcation;    codimension two;   

DOI  :  10.3934/math.2022174

来源: DOAJ

【 摘 要 】

In this paper we revisit a discrete predator-prey model with Holling Ⅳ functional response. By using the method of semidiscretization, we obtain new discrete version of this predator-prey model. Some new results, besides its stability of all fixed points and the transcritical bifurcation, mainly for codimension two 1:1 strong resonance bifurcation, are derived by using the center manifold theorem and bifurcation theory, showing that this system possesses complicate dynamical properties.

【 授权许可】

Unknown