Pattern Evolution in a Predator-Prey System Driven by Cross-Diffusion and Double Allee Effects

YANG Feng; XIAO Min; YANG Zhengwu; DUAN Daifeng; YANG Xinsong; CAO Jinde

doi:10.21656/1000-0887.460002

Volume 47 Issue 1

Jan. 2026

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Article Navigation > Applied Mathematics and Mechanics > 2026 > 47(1): 90-100

YANG Feng, XIAO Min, YANG Zhengwu, DUAN Daifeng, YANG Xinsong, CAO Jinde. Pattern Evolution in a Predator-Prey System Driven by Cross-Diffusion and Double Allee Effects[J]. Applied Mathematics and Mechanics, 2026, 47(1): 90-100. doi: 10.21656/1000-0887.460002

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Pattern Evolution in a Predator-Prey System Driven by Cross-Diffusion and Double Allee Effects

doi: 10.21656/1000-0887.460002

1.
College of Automation and College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, P. R. China
2.
College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, P. R. China
3.
School of Mathematics, Southeast University, Nanjing 211189, P. R. China

Received Date: 2025-01-03
Rev Recd Date: 2025-02-24
Publish Date: 2026-01-01

Abstract

Abstract

The Holling- Ⅱ functional responses and an improved Leslie-Gower term were considered to establish a cross-diffusion predator-prey model with double Allee effects. The existence and stability of positive equilibrium points were analyzed in the absence of diffusion to provide conditions for Turing instability under the diffusion effects. The influential mechanisms of the double Allee effects on the pattern formation, the structural changes, and the evolutionary speed was mainly investigated. The findings reveal that, in stable diffusion-driven systems, the Allee effects can induce pattern formation; conversely, in unstable systems, the Allee effects can lead to structural changes in patterns. Additionally, the time required for the system to reach stable homogeneous and mixed patterns varies with different Allee effects coefficients, indicating that the Allee effects can significantly alter the evolutionary speed of patterns. Therefore, the double Allee effects plays a crucial role in the formation and evolution of Turing patterns in predator-prey systems.
- double Allee effect,
- cross-diffusion,
- Holling-Ⅱ functional response,
- Leslie-Gower,
- Turing pattern

(Contributed by CAO Jinde, M. AMM Editorial Board)

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References(30)

References

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