An Analysis Of Stability Behaviour For Two Preys And Two Predators Ecological Model

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Published: Dec 20, 2023
DOI: https://doi.org/10.53555/jaz.v44iS8.4353
Keywords:
Prey, Predator, Equilibrium Positions, Positivity, Boundedness, Routh-Hurwitz Criterion, Lyapunov Function.

Main Article Content

A.M. Sarravanaprabhu
M. Gunasekaran

Abstract

This study investigates the dynamic interactions among four species within an ecological framework. The population model describes the cooperative dynamics between two preys and two predators as these species cooperate to fulfill various needs, including food requirements and shelter. Simultaneously, interspecific predation may emerge as distinct species compete for survival within the same habitat. The mathematical model comprises a set of nonlinear differential equations for each prey and predator. A comprehensive exploration of feasible equilibrium positions is undertaken to assess species stability at various stages, considering factors such as positivity and boundedness. Furthermore, the model employs the Routh-Hurwitz Criterion and Lyapunov function to investigate both local and global coexistence states of the species.

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How to Cite
A.M. Sarravanaprabhu, & M. Gunasekaran. (2023). An Analysis Of Stability Behaviour For Two Preys And Two Predators Ecological Model. Journal of Advanced Zoology, 44(S8), 442–462. https://doi.org/10.53555/jaz.v44iS8.4353
Issue
Vol. 44 No. S8 (2023): Mathematics and Applied Sciences
Section
Articles
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This work is licensed under a Creative Commons Attribution 4.0 International License.

Author Biographies

A.M. Sarravanaprabhu

Research Scholar, Department of Mathematics, Sri Subramaniyaswamy Government Arts College, Tiruttani – 631 209, India.

M. Gunasekaran

Department of Mathematics, Sri Subramaniyaswamy Government Arts College, Tiruttani – 631209, India.

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