Spatiotemporal (target) patterns in sub-diffusive predator-prey system with the Caputo operator

• Published in: Chaos, solitons and fractals Vol. 160; p. 112267
• Main Authors: Alqhtani, Manal, Owolabi, Kolade M., Saad, Khaled M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2022
• Subjects: Caputo derivative; Numerical simulations; Predator-prey model; Turing patterns; Numerical simulations; Predator-prey model; Caputo derivative; Turing patterns
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2022.112267

The pattern formation process is closely associated with a class of reaction-diffusion problems arising in mathematical biology and chemistry which has generated a lot of research interests over the years in various fields of applied sciences and engineering. On the other hand, mathematical modeling plays a crucial role in the study of predator-prey spatial interactions in the sense of the Caputo operator. The interest here was based on a number of phenomena ranging from the formation of spatial and temporal patterns in Turing systems. In the present work, two important physical examples that are of current and recurring interests are considered, in which the classical time derivative was modeled with the Caputo fractional derivative leading the system of equations to subdiffusive fractional reaction-diffusion models of predator-prey type. The models are examined for both local and global stability analysis and revealed the condition under which diffusion-driven or Turing instability will occur. Some numerical experiments in one and two dimensions are given to obtain the dynamic richness of spatiotemporal pattern formation. 2010 Mathematics Subject Classification: 34A34, 35A05, 35K57, 65L05, 65M06, 93C10 •The study of subdiffusion reaction-diffusion models to obtain some target spatiotemporal patterns•Modeling of nonlinear dynamical systems with the Caputo fractional derivative•Numerical simulation experiments in one and 2D to explore the dynamic richness of Turing structures