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The Diffusion-Driven Instability for a General Time-Space Discrete Host-Parasitoid Model

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  • Xuetian Zhang
  • Chunrui Zhang
  • Jesus M. Munoz-Pacheco

Abstract

In this paper, we consider a general time-space discrete host-parasitoid model with the periodic boundary conditions. We analyzed and obtained some usual conditions, such as Turing instability occurrence, Flip bifurcation occurrence, and Neimark-Sacker bifurcation occurrence. We also find several multiple bifurcation phenomena, such as 1 : 2 Resonance, Neimark-Sacker-Flip bifurcation, Neimark-Sacker-Neimark-Sacker bifurcation, Neimark-Sacker-Flip-Flip bifurcation, induced by diffusion. In a modified Nicholson-Bailey model, employing the mutual interference and diffusive interaction as bifurcation parameters, there appear route from standing Turing instability to multiple bifurcations by changing diffusive parameters. Some numerical simulations of the modified Nicholson-Bailey model support these corollaries.

Suggested Citation

  • Xuetian Zhang & Chunrui Zhang & Jesus M. Munoz-Pacheco, 2023. "The Diffusion-Driven Instability for a General Time-Space Discrete Host-Parasitoid Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2023, pages 1-30, April.
    • Handle: RePEc:hin:jnddns:7710701
    DOI: 10.1155/2023/7710701
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    Cited by:

    1. Li, Tianhua & Zhang, Xuetian & Zhang, Chunrui, 2024. "Pattern dynamics analysis of a space–time discrete spruce budworm model," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).

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