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Pattern formation in the Holling–Tanner predator–prey model with predator-taxis. A nonstandard finite difference approach

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  • Banda, Heather
  • Chapwanya, Michael
  • Dumani, Phindile

Abstract

A characteristic feature of living organisms is their response to the environment in search for food or reproduction opportunities. This paper is devoted to the investigation of the pattern formation of the Holling-Tanner predator–prey model with predator-taxis. We first summarise the qualitative properties of the model where a threshold for the appearance of pattern formation is specified. Then we design and analyse a coupled nonstandard finite difference and finite volume scheme for the proposed model. Numerical simulations are provided to support theoretical findings.

Suggested Citation

  • Banda, Heather & Chapwanya, Michael & Dumani, Phindile, 2022. "Pattern formation in the Holling–Tanner predator–prey model with predator-taxis. A nonstandard finite difference approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 336-353.
    • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:336-353
    DOI: 10.1016/j.matcom.2022.01.028
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    1. Gambino, G. & Lombardo, M.C. & Sammartino, M., 2012. "Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(6), pages 1112-1132.
    2. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
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    Cited by:

    1. Huisen Zhang, 2024. "Dynamics Behavior of a Predator-Prey Diffusion Model Incorporating Hunting Cooperation and Predator-Taxis," Mathematics, MDPI, vol. 12(10), pages 1-12, May.
    2. Chen, Mengxin & Srivastava, Hari Mohan, 2023. "Stability of bifurcating solution of a predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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