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Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion

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  • Hunki Baek
  • Dong Ick Jung
  • Zhi-wen Wang

Abstract

We investigate spatiotemporal dynamics of a semi-ratio-dependent predator-prey system with reaction-diffusion and zero-flux boundary. We obtain the conditions for Hopf, Turing, and wave bifurcations of the system in a spatial domain by making use of the linear stability analysis and the bifurcation analysis. In addition, for an initial condition which is a small amplitude random perturbation around the steady state, we classify spatial pattern formations of the system by using numerical simulations. The results of numerical simulations unveil that there are various spatiotemporal patterns including typical Turing patterns such as spotted, spot-stripelike mixtures and stripelike patterns thanks to the Turing instability, that an oscillatory wave pattern can be emerged due to the Hopf and wave instability, and that cooperations of Turing and Hopf instabilities can cause occurrence of spiral patterns instead of typical Turing patterns. Finally, we discuss spatiotemporal dynamics of the system for several different asymmetric initial conditions via numerical simulations.

Suggested Citation

  • Hunki Baek & Dong Ick Jung & Zhi-wen Wang, 2013. "Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-14, April.
    • Handle: RePEc:hin:jnddns:657286
    DOI: 10.1155/2013/657286
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    Cited by:

    1. Rana, Sourav & Bhattacharya, Sabyasachi & Samanta, Sudip, 2022. "Spatiotemporal dynamics of Leslie–Gower predator–prey model with Allee effect on both populations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 32-49.

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