Dynamics and Pattern Formation of a Diffusive Predator-prey Model in the Subdiffusive Regime in Presence of Toxicity

Daniel Cassidi Bitang A Ziem; Carlos Lawrence Gninzanlong; Conrad Bertrand Tabi; Timoléon Crépin Kofane

doi:10.20944/preprints202008.0412.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 15 August 2020 / Approved: 19 August 2020 / Online: 19 August 2020 (10:54:11 CEST)

Motivated by the fact that the restrictive conditions for a Turing instability are relaxed in sub- diffusive regime, we investigate the effects of subdiffu- sion in the predator−prey model with toxins under the homogeneous Neumann boundary condition. First, the stability analysis of the corresponding ordinary differ- ential equation is carried out. From this analysis, it fol- lows that stability is closely related to the coefficient of toxicity. In addition, the temporal fractional derivative does not systematically widen the range of parameters to maintain a point in the stability domain. Further- more, we derive the condition which links the Turing instability to the coefficient of toxicity in the subdif- fusive regime. System parameters are varied in order to test our mathematical predictions while comparing them to ecological literature. It turns out that the mem- ory effects, linked to the transport process can, depend- ing on the parameters, either stabilize an ecosystem or make a completely different configuration.

Pattern formation; subdiffusive regime; toxicity

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Dynamics and Pattern Formation of a Diffusive Predator-prey Model in the Subdiffusive Regime in Presence of Toxicity

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