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<p>In this paper, we investigate the spatiotemporal dynamics of a fractional-order predator-prey reaction-diffusion model (frPDE) with Holling-type III functional response. We prove that this is not the integer-order reaction-diffusion model, but the frPDE model exhibits fraction-diffusion-induced instability (i.e., Turing instability), which is induced by the fractional-order and diffusion together. Furthermore, via numerical simulations, the frPDE model dynamics exhibits both fractional-order and diffusion controlled Turing pattern formation, which shows that the dynamics of the frPDE model is not simple, but rich and complex.</p>

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Pattern formation in a fractional-order reaction-diffusion predator-prey model with Holling-III functional response

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月4日

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  • Zhaohua Wu,
  • Zhiming Wang,
  • Yongli Cai,
  • Hongwei Yin,
  • Weiming Wang

摘要

In this paper, we investigate the spatiotemporal dynamics of a fractional-order predator-prey reaction-diffusion model (frPDE) with Holling-type III functional response. We prove that this is not the integer-order reaction-diffusion model, but the frPDE model exhibits fraction-diffusion-induced instability (i.e., Turing instability), which is induced by the fractional-order and diffusion together. Furthermore, via numerical simulations, the frPDE model dynamics exhibits both fractional-order and diffusion controlled Turing pattern formation, which shows that the dynamics of the frPDE model is not simple, but rich and complex.