TY - JOUR
T1 - Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive Fractional Multicomponent System 
AU - Owolabi , Kolade M.
AU - Atangana , Abdon
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 - <p style="text-align: justify;">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.</p>