Advances in Analysis

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

Download PDF (2070 KB) PP. 37 - 51 Pub. Date: January 4, 2018

DOI: 10.22606/aan.2018.31005

Author(s)

Moustafa El-Shahed^*
Department of Mathematics, Faculty of Arts and Sciences Qassim University, P.O. Box 3771, Qassim, Unizah 51911, Saudi Arabia
A. M. Ahmed
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, P.O.Box: 11884, Cairo, Egypt
Ibrahim. M. E. Abdelstar
Quantitative Methods Unit, Faculty of Business and Economics Qassim University, P.O.Box: 6633, Qassim, Buridah 51452, Saudi Arabia

Abstract

In this paper, a fractional-order model for phytoplankton-toxic phytoplanktonzooplankton system is presented. This model consists of three components: phytoplankton, toxic phytoplankton, and zooplankton. The equilibrium points are computed and stability of the equilibrium points is analyzed. In addition, fractional Hopf bifurcation conditions for the model are proposed. The generalized Adams-Bashforth-Moulton method is used to solve and simulate the system of fractional differential equations.

Keywords

Toxic-phytoplankton, zooplankton, fractional order, stability, numerical method

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