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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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  • à Ziem, D.C. Bitang
  • Gninzanlong, C.L.
  • Tabi, C.B.
  • Kofané, T.C.

Abstract

Motivated by the fact that the restrictive conditions for a Turing instability are relaxed in subdiffusive regime, we investigate the effects of subdiffusion in the predator - prey model with toxins under the homogeneous Neumann boundary condition. First, the stability analysis of the corresponding ordinary differential equation is carried out. From this analysis, it follows 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. Furthermore, we derive the condition which links the Turing instability to the coefficient of toxicity in the subdiffusive regime. System parameters are varied in order to test our mathematical predictions while comparing them to ecological literature. It turns out that the memory effects, linked to the transport process can, depending on the parameters, either stabilize an ecosystem or make a completely different configuration.

Suggested Citation

  • à Ziem, D.C. Bitang & Gninzanlong, C.L. & Tabi, C.B. & Kofané, T.C., 2021. "Dynamics and pattern formation of a diffusive predator - prey model in the subdiffusive regime in presence of toxicity," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921005920
    DOI: 10.1016/j.chaos.2021.111238
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    References listed on IDEAS

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    1. CA Barnett & M Bateson & C Rowe, 2007. "State-dependent decision making: educated predators strategically trade off the costs and benefits of consuming aposematic prey," Behavioral Ecology, International Society for Behavioral Ecology, vol. 18(4), pages 645-651.
    2. Craig A. Barnett & John Skelhorn & Melissa Bateson & Candy Rowe, 2012. "Educated predators make strategic decisions to eat defended prey according to their toxin content," Behavioral Ecology, International Society for Behavioral Ecology, vol. 23(2), pages 418-424.
    3. Leena Lindström & Rauno V. Alatalo & Johanna Mappes & Marianna Riipi & Laura Vertainen, 1999. "Can aposematic signals evolve by gradual change?," Nature, Nature, vol. 397(6716), pages 249-251, January.
    4. Ziem, D.C. Bitang A. & Mvogo, A. & Kofané, T.C., 2019. "Effects of transport memory in wave fronts in a bistable reaction–diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 36-46.
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