Chaotic and spatiotemporal oscillations in fractional reaction-diffusion system

Kolade M. Owolabi and Berat Karaagac

Chaos, Solitons & Fractals, 2020, vol. 141, issue C

Abstract: This paper focuses on the design and analysis of an efficient numerical method based on the novel implicit finite difference scheme for the solution of the dynamics of reaction-diffusion models. The work replaces the integer first order derivative in time with the Caputo fractional derivative operator. The dynamics of activator-inhibitor as encountered in chemistry, physics and engineering processes, and predator-prey models are two cases addresses in this study. In order to provide a good guidelines on the correct choice of parameters for the numerical simulation of full fractional reaction-diffusion system, its linear stability analysis is also examined. The resulting scheme is applied to solve cross-diffusion problem in two-dimensions. In the experimental results, a number of spatiotemporal and chaotic patterns that are related to Turing pattern are observed. It was discovered in the simulation experiments that the species predator-prey model distribute in almost same fashion, while that of the activator-inhibitor dynamics behaved differently regardless of the value of fractional order chosen.

Keywords: Activator-inhibitor model; Caputo fractional derivative; Predator-prey system; Chaotic and spatiotemporal patterns; Numerical simulations (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920306986

DOI: 10.1016/j.chaos.2020.110302

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