Bifurcation of a discrete predator-prey model with increasing functional response and constant-yield prey harvesting

Jiange Dong; Xianyi Li; Jiange Dong; Xianyi Li

doi:10.3934/era.2022200

Electronic Research Archive

2022, Volume 30, Issue 10: 3930-3948. doi: 10.3934/era.2022200

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Bifurcation of a discrete predator-prey model with increasing functional response and constant-yield prey harvesting

Jiange Dong ,
Xianyi Li ^,

Department of Big Data Science, School of Science Zhejiang University of Science and Technology, Hangzhou 310023, China

Academic Editor: Fengqi Yi

Received: 06 July 2022 Revised: 02 August 2022 Accepted: 10 August 2022 Published: 30 August 2022

Using the forward Euler method, we derive a discrete predator-prey system of Gause type with constant-yield prey harvesting and a monotonically increasing functional response in this paper. First of all, a detailed study for the existence and local stability of fixed points of the system is obtained by invoking an important lemma. Mainly, by utilizing the center manifold theorem and the bifurcation theory some sufficient conditions are obtained for the saddle-node bifurcation and the flip bifurcation of this system to occur. Finally, with the use of Matlab software, numerical simulations are carried out to illustrate the theoretical results obtained and reveal some new dynamics of the system-chaos occuring.
- discrete predator-prey system,
- forward Euler method,
- flip bifurcation,
- saddle-node bifurcation,
- center manifold theorem
Citation: Jiange Dong, Xianyi Li. Bifurcation of a discrete predator-prey model with increasing functional response and constant-yield prey harvesting[J]. Electronic Research Archive, 2022, 30(10): 3930-3948. doi: 10.3934/era.2022200

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Abstract

Using the forward Euler method, we derive a discrete predator-prey system of Gause type with constant-yield prey harvesting and a monotonically increasing functional response in this paper. First of all, a detailed study for the existence and local stability of fixed points of the system is obtained by invoking an important lemma. Mainly, by utilizing the center manifold theorem and the bifurcation theory some sufficient conditions are obtained for the saddle-node bifurcation and the flip bifurcation of this system to occur. Finally, with the use of Matlab software, numerical simulations are carried out to illustrate the theoretical results obtained and reveal some new dynamics of the system-chaos occuring.

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