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Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive Fractional Multicomponent System

Part of: Numerical analysis: Ordinary differential equations Control systems Parabolic equations and systems Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  28 November 2017

Kolade M. Owolabi  and
Abdon Atangana
Kolade M. Owolabi*
Affiliation:
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
Abdon Atangana*
Affiliation:
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
*
*Corresponding author. Emails:mkowolax@yahoo.com (K. M. Owolabi), abdonatangana@yahoo.fr (A. Atangana)
*Corresponding author. Emails:mkowolax@yahoo.com (K. M. Owolabi), abdonatangana@yahoo.fr (A. Atangana)
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Abstract

In this work, we examine the mathematical analysis and numerical simulation of pattern formation in a subdiffusive multicomponents fractional-reaction-diffusion system that models the spatial interrelationship between two preys and predator species. The major result is centered on the analysis of the system for linear stability. Analysis of the main model reflects that the dynamical system is locally and globally asymptotically stable. We propose some useful theorems based on the existence and permanence of the species to validate our theoretical findings. Reliable and efficient methods in space and time are formulated to handle any space fractional reaction-diffusion system. We numerically present the complexity of the dynamics that are theoretically discussed. The simulation results in one, two and three dimensions show some amazing scenarios.

Keywords

Asymptotically stablecoexistenceFourier spectral methodnumerical simulationspredator-preyfractional multi-species system

MSC classification

Secondary: 35K57: Reaction-diffusion equations 65L05: Initial value problems 65M06: Finite difference methods 93C10: Nonlinear systems
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 6 , December 2017 , pp. 1438 - 1460
Copyright
Copyright © Global-Science Press 2017 

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