Dynamics of a predator-prey model with fear effects and gestation delays

Yaping Wang; Yuanfu Shao; Chuanfu Chai; Yaping Wang; Yuanfu Shao; Chuanfu Chai

doi:10.3934/math.2023378

AIMS Mathematics

2023, Volume 8, Issue 3: 7535-7559. doi: 10.3934/math.2023378

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Research article

Dynamics of a predator-prey model with fear effects and gestation delays

College of Science, Guilin University of Technology, Guilin, Guangxi 541004, China

Received: 12 November 2022 Revised: 06 January 2023 Accepted: 10 January 2023 Published: 17 January 2023
MSC : 34C23, 92D25

Recent studies have shown that, in addition to direct predation, fear of predators alters the physiological behavior of prey. Based on this fact, this paper investigates a three-species food chain based on ratio-dependent and Beddington-DeAngelis type functional responses, which incorporates fear effects and two gestation delays. The positivity, boundedness and existence of equilibrium points of the system are investigated, and the local stability behavior of the equilibrium points and the occurrence of Hopf-bifurcation when the time lag parameters exceed the critical values are studied by analyzing the corresponding characteristic equations. The main results show that Hopf-bifurcation occurs when the time delay parameters attain the thresholds. Finally, numerical simulations are performed to verify our main results.
- food chain model,
- fear effect,
- delays,
- stability analysis,
- Hopf-bifurcation
Citation: Yaping Wang, Yuanfu Shao, Chuanfu Chai. Dynamics of a predator-prey model with fear effects and gestation delays[J]. AIMS Mathematics, 2023, 8(3): 7535-7559. doi: 10.3934/math.2023378

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Abstract

Recent studies have shown that, in addition to direct predation, fear of predators alters the physiological behavior of prey. Based on this fact, this paper investigates a three-species food chain based on ratio-dependent and Beddington-DeAngelis type functional responses, which incorporates fear effects and two gestation delays. The positivity, boundedness and existence of equilibrium points of the system are investigated, and the local stability behavior of the equilibrium points and the occurrence of Hopf-bifurcation when the time lag parameters exceed the critical values are studied by analyzing the corresponding characteristic equations. The main results show that Hopf-bifurcation occurs when the time delay parameters attain the thresholds. Finally, numerical simulations are performed to verify our main results.

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