Abstract
In this paper, a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed. The interaction between prey, middle predator and top predator population is investigated. In order to clarify the characteristics of the proposed model, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions of the proposed model are examined. Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained. By using stability analysis of the fractional-order system, it is proved that if the basic reproduction number , the predator free equilibrium point is globally asymptotically stable. The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem. Some numerical examples are given to illustrate the theoretical findings. The impact of harvesting on prey and the middle predator is studied. We conclude that harvesting parameters can control the dynamics of the middle predator. A numerical approximation method is developed for the proposed stochastic fractional-order model.
Highlights
Mathematical analysis is one of the important tools for understanding and interpreting different interactions in the environment around us
CMC, 2022, vol.70, no.2 of this paper is to study the deterministic and stochastic fractional-order Hastings-Powell model incorporating harvesting
It is shown that the proposed model has bounded and non-negative solution as desired in any population dynamics
Summary
Mathematical analysis is one of the important tools for understanding and interpreting different interactions in the environment around us. The stochastic models may be a more appropriate way of modeling the Hastings-Powell food chain model in many circumstances [17,18]. CMC, 2022, vol., no.2 of this paper is to study the deterministic and stochastic fractional-order Hastings-Powell model incorporating harvesting. A numerical approximation method is developed for the proposed stochastic fractional-order model. The paper is arranged as follows: In Section 2, the mathematical model is described.
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