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Time Evolution of the Densities of Three Species Interacting in the Same Ecosystem and the Stability Analysis of Steady States for a Reaction–Diffusion PDE Model

Author

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  • Emmanuel Niyigaba
  • Wellars Banzi
  • Hamidou Touré
  • Mariano Torrisi

Abstract

This paper investigates the trends of three different species interacting in the same ecosystem. The study is conducted on the ecosystem which consists of a prey S1 and two predators S2 and S3 in such a way that S2 is a predator of S1 and S3 is a predator of both S1 and S2. In addition, S1 and S2 share the same food which is the main food for S1 and the alternative food for S2. A system of three simultaneous nonlinear partial differential equations is used to represent this situation. The local stability of all constant equilibrium points is discussed after showing their feasibility. In addition, a condition for which a coexisting constant equilibrium point is asymptotically globally stable is also investigated. The results showed that the system has eight constant equilibrium points. Five of them are unstable, while the three remaining are asymptotically locally stable under some conditions on the parameters that are involved in the model.

Suggested Citation

  • Emmanuel Niyigaba & Wellars Banzi & Hamidou Touré & Mariano Torrisi, 2024. "Time Evolution of the Densities of Three Species Interacting in the Same Ecosystem and the Stability Analysis of Steady States for a Reaction–Diffusion PDE Model," Journal of Applied Mathematics, Hindawi, vol. 2024, pages 1-16, September.
    • Handle: RePEc:hin:jnljam:9635236
    DOI: 10.1155/2024/9635236
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