Dynamical Behavior of Three Species Model with Holling Type Functional Response in the Presence of Logistic Growth

Divya  B; Kavitha  K

doi:10.6180/jase.202501_28(1).0010

Dynamical Behavior of Three Species Model with Holling Type Functional Response in the Presence of Logistic Growth

Mathematics / Statistics

Divya B¹ and Kavitha K²This email address is being protected from spambots. You need JavaScript enabled to view it.

¹Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India

²Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India

Received: October 10, 2023
Accepted: January 1, 2024
Publication Date: March 23, 2024

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202501_28(1).0010

In this article, we investigate a three-species ecosystem including prey(x), predator(y) and super predator (z) in a linear food chain model. Depending on these three species, we created three different models which are based on the Lotka-Volterra Model. Differential equations are used to determine the interaction between these species. The predator chases prey, and the super predator hunts the predator because the model of these systems is linear. Additionally, we include Holling-type functional responses, such as Holling type I for model I and Holling type II for both models II and III. In all these models the Prey has a logistic growth. The existence of the possible equilibrium points has been identified. The Variational matrix method is used to examine the dynamic behavior of these models. Further, the stability of these models is carried out using the Descartes rule. Computational simulations are used to demonstrate analytic results using Matlab software. The behavior of these models is visualised around the equilibrium point. These model phase diagrams are also obtained.

Keywords: Equilibrium Points; Functional Response; Logistic Growth; Stability Analysis; Three Species Model; Variational Matrix.

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