Numerical Solution of a Fractional-Order Predator-Prey Model with Prey Refuge and Additional Food for Predator

Rio Satriyantara,Noor Hidayat,Agus Suryanto

doi:10.21776/ub.jels.2018.008.01.11

Rio Satriyantara, Noor Hidayat + Show 1 more

Open Access

https://doi.org/10.21776/ub.jels.2018.008.01.11

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Abstract

In this paper, a fractional-order predator-prey model with prey refuge and additional food for predator is solved numerically. For that aim, the model is discretized using a piecewise constant arguments. The equilibrium points of the discrete fractional-order model are investigated. Numerical simulations are conducted to see the stability of each equilibrium point. The numerical simulations show that stability of the equilibrium points is dependent on the time step. Keywords: Additional Food, Fractional-Order, Predator-Prey, Prey Refuge.

Highlights

In ecology, understanding the dynamical relationship between prey and predator are center of goal [1]
In 1928, Lotka [3] and Volterra [4] studied the relationship between prey and predator introduced a predator-prey model
Axial equilibrium point and coexisting equilibrium point with and Systematically, predator-prey model forms a system of first-order differential equations

Summary

INTRODUCTION

In ecology, understanding the dynamical relationship between prey and predator are center of goal [1]. Ghosh et al introduced the following prey-predator model with prey refuge and additional food for predator [5]. In the second part of right-hand-side the prey population, parameter characterize as predation rate on prey by modified functional respon Holling-type II. The refuge on prey is exhibit in order to avoid the extinction of prey population caused by predation. Axial equilibrium point and coexisting equilibrium point with and Systematically, predator-prey model forms a system of first-order differential equations. As a generalization of integerorder differential equation, the fractional-order exhibit dynamic behaviors, such as period- orbits [10]. The aim of this study is to give an overview of population densities based on numerical simulations of the discrete fractional-order model

MATERIAL AND METHOD Discrete Model

AND DISCUSSION

The co-existing equilibrium point with

Findings

CONCLUSION