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Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth

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  • Bo Yang

Abstract

The spatiotemporal dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth subject to zero-flux boundary condition are investigated analytically and numerically. The asymptotic stability of the positive equilibrium and the existence of Hopf bifurcation around the positive equilibrium are shown; the conditions of Turing instability are obtained. And with the help of numerical simulations, it is found that the model exhibits complex pattern replication: stripes, spots-stripes mixtures, and spots Turing patterns.

Suggested Citation

  • Bo Yang, 2013. "Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-8, March.
    • Handle: RePEc:hin:jnddns:454209
    DOI: 10.1155/2013/454209
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    Cited by:

    1. Kumar, Vikas, 2024. "Pattern formation and delay-induced instability in a Leslie–Gower type prey–predator system with Smith growth function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 78-97.

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