Analysis of a prey-predator system incorporating the additive Allee effect and intraspecific cooperation

Yalong Xue; Yalong Xue

doi:10.3934/math.2024063

AIMS Mathematics

2024, Volume 9, Issue 1: 1273-1290. doi: 10.3934/math.2024063

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Research article

Analysis of a prey-predator system incorporating the additive Allee effect and intraspecific cooperation

Yalong Xue ^,

College of Mathematics and Physics, Ningde Normal University, Ningde 352100, Fujian, China

Received: 30 September 2023 Revised: 18 November 2023 Accepted: 26 November 2023 Published: 07 December 2023
MSC : 34C23, 34D23

To understand the influence of the Allee effect and intraspecific cooperation on the dynamics of a predator-prey system, we constructed a model using ordinary differential equations. Our research shows that the system exhibits more complex dynamics, including possible bistability between alternative semi-trivial states and an Allee effect for prey. The Allee effect can destabilize the system. The equilibrium points of the system could change from stable to unstable. Otherwise, even if the system were stable, it would take much longer time to reach a stable state. We also find that the presence of the Allee effect of prey increases the positive equilibrium density of the predator but has no effect on the positive equilibrium density of the prey. It should be noted that the influence of nonlinear predator mortality also causes the system to take a longer time to reach a steady state.
- prey-predator,
- Allee effect,
- intraspecific cooperation,
- stability,
- bifurcation
Citation: Yalong Xue. Analysis of a prey-predator system incorporating the additive Allee effect and intraspecific cooperation[J]. AIMS Mathematics, 2024, 9(1): 1273-1290. doi: 10.3934/math.2024063

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Abstract

To understand the influence of the Allee effect and intraspecific cooperation on the dynamics of a predator-prey system, we constructed a model using ordinary differential equations. Our research shows that the system exhibits more complex dynamics, including possible bistability between alternative semi-trivial states and an Allee effect for prey. The Allee effect can destabilize the system. The equilibrium points of the system could change from stable to unstable. Otherwise, even if the system were stable, it would take much longer time to reach a stable state. We also find that the presence of the Allee effect of prey increases the positive equilibrium density of the predator but has no effect on the positive equilibrium density of the prey. It should be noted that the influence of nonlinear predator mortality also causes the system to take a longer time to reach a steady state.

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