JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (4): 104-117.doi: 10.6040/j.issn.1671-9352.0.2023.511

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Dynamical analysis in a diffusive predator-prey model with cooperative hunting and group defense

XU Yingting, ZHAO Jiantao, WEI Xin*   

  1. School of Mathematical Science, Heilongjiang University, Harbin 150080, Heilongjiang, China
  • Published:2025-04-08

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Abstract: In this paper, we propose a diffusive predator-prey model with cooperative hunting and group defense, and investigate the existence of Turing instability and Turing-Hopf bifurcation induced by diffusion. Taking coefficient of diffusion as bifurcation parameter, we analyze the stability of the coexistence equilibrium, and explore the complex dynamical behaviours of the system by calculating the normal forms near the Turing-Hopf bifurcation points. Moreover, we carry out some numerical simulations to illustrate the theoretical analysis. Our study shows that the system demonstrates complex dynamical behaviours near the Turing-Hopf bifurcation point, including steady-state solutions, homogeneous periodic solutions, non-homogeneous steady-state solutions, and non-homogeneous periodic solutions.

Key words: cooperative hunting, group defense, Turing-Hopf bifurcation, diffusion, predator-prey model

CLC Number: 

  • O175
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