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Diffusion driven instability and Hopf bifurcation in spatial predator-prey model on a circular domain

Author

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  • Abid, Walid
  • Yafia, Radouane
  • Aziz-Alaoui, M.A.
  • Bouhafa, Habib
  • Abichou, Azgal

Abstract

In this paper, we investigate theoretically and numerically a 2-D spatio-temporal dynamics of a predator-prey mathematical model which incorporates the Holling type II and a modified Leslie–Gower functional response and logistic growth of the prey. This system is modeled by a reaction diffusion equations defined on a disc domain {(x,y)∈R2/x2+y2

Suggested Citation

  • Abid, Walid & Yafia, Radouane & Aziz-Alaoui, M.A. & Bouhafa, Habib & Abichou, Azgal, 2015. "Diffusion driven instability and Hopf bifurcation in spatial predator-prey model on a circular domain," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 292-313.
    • Handle: RePEc:eee:apmaco:v:260:y:2015:i:c:p:292-313
    DOI: 10.1016/j.amc.2015.03.070
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    Cited by:

    1. Verdière, Nathalie & Manceau, David & Zhu, Shousheng & Denis-Vidal, Lilianne, 2020. "Inverse problem for a coupling model of reaction-diffusion and ordinary differential equations systems. Application to an epidemiological model," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    2. Huang, Tousheng & Zhang, Huayong, 2016. "Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 92-107.
    3. Zhang, Huayong & Ma, Shengnan & Huang, Tousheng & Cong, Xuebing & Yang, Hongju & Zhang, Feifan, 2018. "A new finding on pattern self-organization along the route to chaos," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 118-130.
    4. Anita Triska & Agus Yodi Gunawan & Nuning Nuraini, 2023. "The Effects of the Susceptible and Infected Cross-Diffusion Terms on Pattern Formations in an SI Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
    5. Wang, Jinliang & Li, You & Zhong, Shihong & Hou, Xiaojie, 2019. "Analysis of bifurcation, chaos and pattern formation in a discrete time and space Gierer Meinhardt system," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 1-17.
    6. Kumari, Sarita & Tiwari, Satish Kumar & Upadhyay, Ranjit Kumar, 2022. "Cross diffusion induced spatiotemporal pattern in diffusive nutrient–plankton model with nutrient recycling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 246-272.

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