DELAY DIFFUSIVE PREY PREDATOR MODEL WITH HUNTING COOPERATION IN PREDATORS

Articles in Press

Document Type : Research Paper

Authors

1 Department of Applied Science and Humanities, Government Engineering College, Siwan.

2 Department of Geology, Government Engineering College, Siwan.

Abstract

In this paper, we conduct a detailed stability analysis and investigate the occurrence of Hopf bifurcation in a temporal predator-prey model that incorporates hunting cooperation among predators. Building on this, we extend the model to a spatiotemporal domain to explore how spatial diffusion influences the dynamics. Our simulations reveal the emergence of distinct spatial patterns, such as cold spots indicating regions of low prey density and hot spots corresponding to high predator concentration. Notably, we observe that increasing the diffusion rates leads to the formation of more sharply concentrated and spatially structured patterns. To further enrich the model, we introduce a time delay representing the gestation or response time in predator-prey interactions. The inclusion of delay significantly alters the dynamics: while the non-delayed model supports stationary spatial patterns, the delayed model gives rise to complex oscillatory structures that evolve over time, highlighting the critical role of delay in generating temporal fluctuations in pattern formation.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 25 August 2025

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History

  • Receive Date: 18 October 2024
  • Revise Date: 25 May 2025
  • Accept Date: 24 August 2025

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