Modelling and formation of spatiotemporal patterns of fractional predation system in subdiffusion and superdiffusion scenarios
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa
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Accepted: 8 January 2018
Published online: 12 February 2018
This paper primarily focused on the question of how population diffusion can affect the formation of the spatial patterns in the spatial fraction predator-prey system by Turing mechanisms. Our numerical findings assert that modeling by fractional reaction-diffusion equations should be considered as an appropriate tool for studying the fundamental mechanisms of complex spatiotemporal dynamics. We observe that pure Hopf instability gives rise to the formation of spiral patterns in 2D and pure Turing instability destroys the spiral pattern and results to the formation of chaotic or spatiotemporal spatial patterns. Existence and permanence of the species is also guaranteed with the 3D simulations at some instances of time for subdiffusive and superdiffusive scenarios.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018