Volume 9, Issue 6
Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive Fractional Multicomponents System

Kolade M. Owolabi & Abdon Atangana

Adv. Appl. Math. Mech., 9 (2017), pp. 1438-1460.

Published online: 2017-09

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  • Abstract

In this work, we examine the mathematical analysis and numerical simulation of pattern formation in a subdiffusive multicomponents fractional-reactiondiffusion 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 stable, coexistence, Fourier spectral method, numerical simulations, predator-prey, fractional multi-species system.

  • AMS Subject Headings

35A05, 35K57, 65L05, 65M06, 93C10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-1438, author = {}, title = {Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive Fractional Multicomponents System }, journal = {Advances in Applied Mathematics and Mechanics}, year = {2017}, volume = {9}, number = {6}, pages = {1438--1460}, abstract = {

In this work, we examine the mathematical analysis and numerical simulation of pattern formation in a subdiffusive multicomponents fractional-reactiondiffusion 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0115}, url = {http://global-sci.org/intro/article_detail/aamm/10187.html} }
TY - JOUR T1 - Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive Fractional Multicomponents System JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1438 EP - 1460 PY - 2017 DA - 2017/09 SN - 9 DO - http://doi.org/10.4208/aamm.OA-2016-0115 UR - https://global-sci.org/intro/article_detail/aamm/10187.html KW - Asymptotically stable, coexistence, Fourier spectral method, numerical simulations, predator-prey, fractional multi-species system. AB -

In this work, we examine the mathematical analysis and numerical simulation of pattern formation in a subdiffusive multicomponents fractional-reactiondiffusion 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.

Kolade M. Owolabi & Abdon Atangana. (2020). Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive Fractional Multicomponents System . Advances in Applied Mathematics and Mechanics. 9 (6). 1438-1460. doi:10.4208/aamm.OA-2016-0115
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