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

Feiyu Shi; Yulong Li; Deng Zhao; Feiyu Shi; Yulong Li; Deng Zhao

doi:10.3934/math.2026463

AIMS Mathematics

2026, Volume 11, Issue 4: 11258-11295. doi: 10.3934/math.2026463

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

1.
School of Artificial Intelligence, China University of Geosciences (Beijing), 10083 Beijing, China
2.
School of Mathematical Sciences, Beihang University, 100191 Beijing, China

Received: 30 January 2026 Revised: 26 March 2026 Accepted: 31 March 2026 Published: 22 April 2026
MSC : 39A28, 39A30, 39A60

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.
- predator-prey model,
- Hopf bifurcation,
- Bogdanov-Takens bifurcation,
- anti-predator behavior,
- numerical simulations
Citation: Feiyu Shi, Yulong Li, Deng Zhao. Predator-prey model with additional food inducing competition among predators incorporating anti-predator behavior[J]. AIMS Mathematics, 2026, 11(4): 11258-11295. doi: 10.3934/math.2026463

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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.

References

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