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Abstract

This research proposes a mathematical model to investigate the dynamical behavior of the system of three species, namely prey, predator and top predator. The feeding behavior of each predator serves as a functional response. The interaction between the species is carried out by a functional response. Crowley Martin functional response is incorporated between prey and predator while Holling type III functional response occurs between predator and top predator. The existence of positivity and boundedness of the system have been examined. The equilibrium points of the system are determined. The system has been linearized by applying the Jacobian matrix. The main perspective used to discuss the system's dynamics is that of permanence and stability. Further stability analysis of the system is carried out at around each equilibrium point. To comprehend the dynamics of the model system, the asymptotic stability of several equilibrium solutions, both local and global, is investigated. Routh Hurwitz criteria are used to analyze local stability at every equilibrium point. Using an appropriate Lyapunov function, the global asymptotic stability of the positive interior equilibrium solution is established. From a biological perspective, a system is considered to be permanent if all of its populations continue to exist in the future. The existence of permanence conditions of the system have been determined. To support the analytical results, several numerical simulations are carried out using the MATLAB software. Finally based on the results of the analytical and numerical simulations, the impact of the functional response between the prey, predator and top predator was discussed.

Keywords

Food chain model, Functional response, Global stability, Jacobian matrix, Logistic growth, Stability analysis

Subject Area

Mathematics

First Page

632

Last Page

645

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Receive Date

10-24-2023

Revise Date

4-28-2024

Accept Date

4-30-2024

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