Chinese Quarterly Journal of Mathematics >

2024 , Vol. 39 >Issue 2: 128 - 143

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.02.002

Codimension-Two Bifurcations Analysis of a Discrete Predator-Prey Model Incorporating a Prey Refuge

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  • College of Science, Xi’an Polytechnic University, Xi’an 710600, China
PANG Ru-yi (1998-), female, native of Zhoukou, Henan, graduate student of Xi’an Polytechnic University, engages in biomathematics; CHEN Qiao-ling (1987-), female, native of Xi’an, Shaanxi, professor of Xi’an Polytechnic University, engages in biomathematics.

Received date: 2023-07-14

  Online published: 2024-06-30

Supported by

Supported by the National Natural Science Foundation of China (Grant No. 12271421); The Shaanxi Province Innovation Talent Promotion Plan Project (Grant No. 2023KJXX-056).

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Abstract

 In this paper, a discrete predator-prey model with prey refuge is investigated. It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and 1:3 resonances. The bifurcation diagrams and phase portraits show that the model has some interesting complex dynamical behaviors, such as limit cycle, periodic solutions, chaos and codimension-1 bifurcations.

Key words：  Refuge; Discrete predator-prey model; Codimension-2 bifurcations; Chaos

Cite this article

PANG Ru-yi, CHEN Qiao-ling . Codimension-Two Bifurcations Analysis of a Discrete Predator-Prey Model Incorporating a Prey Refuge[J]. Chinese Quarterly Journal of Mathematics, 2024 , 39(2) : 128 -143 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.002

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