Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive Fractional Multicomponent System
Year: 2017
Author: Kolade M. Owolabi, Abdon Atangana
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 6 : pp. 1438–1460
Abstract
In this work, we examine the mathematical analysis and numerical simulation of pattern formation in a subdiffusive multicomponent 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2016-0115
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 6 : pp. 1438–1460
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Asymptotically stable coexistence Fourier spectral method numerical simulations predator-prey fractional multi-species system.