Analytical derivation of delayed prey–predator model with hunting-and-resting delay

Mostafa Adimy and Malay Banerjee

Chaos, Solitons & Fractals, 2025, vol. 195, issue C

Abstract: We investigate a prey–predator model based on a general Gause type system. We take for the predator two phases into account, the hunting phase and the resting one. We suppose that the predators stop hunting after they catch the prey. Then they enter the resting phase where they stay for a fixed limited time. The resulting mathematical model is a system of two age-structured partial differential equations. By integrating this system over age and using the characteristics method, we reduce it to a delay differential system, and we investigate the existence and stability of the steady states. In particular, we have shown that the introduction of the delay (the duration of the resting phase) stabilizes the coexistence equilibrium.

Keywords: Delay differential equation; Age-structure PDE; Prey–predator; Stability; Hopf bifurcation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:195:y:2025:i:c:s0960077925002851

DOI: 10.1016/j.chaos.2025.116272

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