Dynamics of a three species syn-ecological ammensalsim model: A stochastic approach

K. Kondala Rao^a, K. Lakshmi Narayan^a, G. Ranjith Kumar^b, K. Ramesh^b, A. V. Papa Rao<sup>c

a</sup> Vidya Jyothi Institute of Technology (VJIT), Hyderabad, Telangana, India
^b Department of Mathematics, Anurag University, Hyderabad 500088, Telangana, India
^c Department of Mathematics, JNTU-GV, COE-Vizianagaram, Andhra Pradesh, India

Abstract: We study the three-species system in which the species of the first kind is neutral to the species of the third kind and ammensal to the species of the second kind. We give an analytic analysis of the model. A collection of first-order nonlinear ordinary differential equations characterizes the model. The stability criteria of the interior equilibrium state are discussed. Additionally, an exact solution of the perturbed equations is determined. A stochastic process is used to illustrate the model stability. MatLab is used to do numerical simulation to support the analytic conclusions.

Keywords: first-, second-, and third-kind species, neutral, ammensal, equilibrium points, stability analysis, stochastic processes.

MSC: 34DXX, 34NXX, 97MXX, 34D23& 37B25

Received: 28.01.2025
Revised: 25.02.2025

DOI: 10.4213/tmf10911

 English version: Theoretical and Mathematical Physics, 2025, 223:3, 944–951

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