Analysis and pattern formation scenarios in the superdiffusive system of predation described with Caputo operator. (November 2021) - Owolabi, Kolade M.; Pindza, Edson; Atangana, Abdon
Highlights: Numerical technique based on spline method for spatial approximation. Improved exponential time-differencing which incorporated the Pade approximations to exponential function. Main reaction-diffusion model of predator-prey type in Caputo sense. Linear (local and global) stability analysis. Turing pattern formation in superdiffusion process. Numerical simulation and results in one and two dimensions.<?Qry msg="Au: There should be between three and five individual highlights in the article. - Each individual highlight must not exceed 125 characters."?> Abstract: The concept of a fractional derivative is introduced to the predator-prey system to describe the species anomalous superdiffusive process. To achieve this, a new class of predator-prey model with the Beddington-DeAngelis functional response is formulated in the sense of the Caputo fractional order operator. This work aims to give a mathematical basis for computational studies of a two-variable fractional reaction-diffusion system in one and two dimensions from biological and numerical perspectives. As a result, some details of the local and global dynamics of the reaction-diffusion system are provided by using the idea of the linear stability analysis and well-known dynamical systems theory to derive conditions on the parameters which can guarantee biologically meaningful equilibria also serve as a guide in ensuring the correct choice of parameters when numerically experimenting with the solutions of the full fractional reaction-diffusion model. The behavior of the new dynamical system is examined for both diffusive and non-diffusive systems at different instances of fractional order.