Geometric Approach to Predator-Prey Model with Carrying Capacity on Prey Population

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Abstract

In this paper, we explore a classical predator-prey model where the birth rate of the prey is significantly lower than the mortality rate of the predators, while also considering a limited prey population. We incorporate an environmental carrying capacity factor for the prey to account for this. Given the different timescales of the predator and prey populations, some system solutions may exhibit a fast-slow structure. We analyze this fast-slow behavior using geometric singular perturbation theory (GSPT), which allows us to separate the system into fast and slow subsystems. Our research investigates the existence and stability of equilibrium solutions and the behavior of solutions near the critical manifold. Additionally, we use an entry-exit function to analytically establish the connection between the solutions of the slow subsystem and those of the fast subsystem.

Original languageEnglish
Pages (from-to)162-176
Number of pages15
JournalCommunication in Biomathematical Sciences
Volume7
Issue number2
DOIs
Publication statusPublished - 18 Dec 2024

Keywords

  • entry-exit function
  • fast-slow system
  • geometric singular perturbation theory
  • Predator-prey

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