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Research Article | Open Access

Predator-prey model with additional food inducing competition among predators incorporating anti-predator behavior

Feiyu Shi1, Yulong Li2, Deng Zhao1( )
School of Artificial Intelligence, China University of Geosciences (Beijing), 10083 Beijing, China
School of Mathematical Sciences, Beihang University, 100191 Beijing, China
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Abstract

The dynamical behavior of a predator-prey model with additional food inducing competition among predators incorporating anti-predator behavior is analyzed in this paper. The existence, stability, and local dynamics of the equilibria are discussed. By using bifurcation theory, we studied the existence of Hopf bifurcation and Bogdanov-Takens bifurcation. The numerical simulations are presented to illustrate the results of the theoretical analysis, and complex dynamical behaviors were found, such as limit cycles and homoclinic cycles.

Keywords

predator-prey modelHopf bifurcationBogdanov-Takens bifurcationanti-predator behaviornumerical simulations
CLC number: 39A28, 39A30, 39A60

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AIMS Mathematics
Volume 11 Issue 4,
April 2026
Pages 11258-11295
DOI: 10.3934/math.2026463

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Cite this article:
Shi F, Li Y, Zhao D. Predator-prey model with additional food inducing competition among predators incorporating anti-predator behavior. AIMS Mathematics, 2026, 11(4): 11258-11295. https://doi.org/10.3934/math.2026463

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Received: 30 January 2026
Revised: 26 March 2026
Accepted: 31 March 2026
Published: 22 April 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)