BIFURCATION ANALYSIS AND CHAOS CONTROL OF DISCRETE PREDATOR–PREY MODEL WITH ADDITIVE ALLEE EFFECT
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Published:2023-11-21
Issue:04
Volume:31
Page:1477-1505
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ISSN:0218-3390
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Container-title:Journal of Biological Systems
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language:en
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Short-container-title:J. Biol. Syst.
Author:
LI HANGHANG1ORCID,
HU XINLI1ORCID
Affiliation:
1. School of Science, Xi’an Polytechnic University, Xi’an 710048, P. R. China
Abstract
This paper presents a study of a discrete prey–predator model with additive Allee effect. The model is discretized using the forward Euler method, and the system is analyzed using bifurcation theory and chaos control. The equilibrium point of the discrete system is obtained through equilibrium analysis, and the stability of the equilibrium point is determined by analyzing the parameter conditions. The study also establishes the existence and direction of Neimark–Sacker bifurcation at the positive equilibrium point. The paper proposes two control strategies to manage chaotic behavior and Neimark–Sacker bifurcation: exponential control and hybrid feedback control. These control methods are demonstrated to be effective in controlling the chaotic behavior and bifurcation of the system through numerical simulation. Overall, the results of the study provide important insights into the dynamics of the discrete prey–predator model with additive Allee effect, as well as effective methods for controlling chaos and bifurcation in the system.
Funder
National Natural Science Foundation of China
Scientific Research Program funded by Shaanxi Provincial Education Department
China Scholarship Council
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Ecology,Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Ecology