Abstract
In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model.
Highlights
The most influential theme in ecology and mathematical modeling is the dynamic of the relationship among species
The increasing of mathematical models that based on fractional order differential equation has recently obtained popularity in the studying the behavior of biological models
Fractional-order differential equation has been successfully used and applied to model many areas of science, engineering, and phenomena that cannot be formulated by other types of equations [10, 16]
Summary
The most influential theme in ecology and mathematical modeling is the dynamic of the relationship among species. Many authors extended or modified the work of the Lotka and Voltera model [1, 2], and they have investigated thse topics widely by using ordinary differential equations or deference equations, see [3,4,5,6,7,8,9], and references therein Nowadays, authors formulate their mathematical models by fractional order differential equation due to their ability to give the precise description for various linear and nonlinear phenomena [10,11,12,13,14,15].
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