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Spatial dynamics of a fractional predator-prey system with time delay and Allee effect

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  • Bi, Zhimin
  • Liu, Shutang
  • Ouyang, Miao

Abstract

In this paper, we investigate the spatial dynamics of a class of spatial fractional predator-prey systems with time delay and Allee effect. Firstly, Hopf bifurcation and Turing bifurcation conditions are obtained by using stability theory and bifurcation theory. Then, the abundant dynamic behaviors of the system are demonstrated by numerical simulation. Finally, numerical results show that time delay, Allee effect, and fractional diffusion can affect the formation 3D Turing patterns such as spherical, tube, spherical and tube coexisting and the constitution of 3D spiral wave patterns.

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  • Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Spatial dynamics of a fractional predator-prey system with time delay and Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006440
    DOI: 10.1016/j.chaos.2022.112434
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    Cited by:

    1. Owolabi, Kolade M. & Jain, Sonal, 2023. "Spatial patterns through diffusion-driven instability in modified predator–prey models with chaotic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Zhang, Huayong & Guo, Fenglu & Zou, Hengchao & Zhao, Lei & Wang, Zhongyu & Yuan, Xiaotong & Liu, Zhao, 2024. "Refuge-driven spatiotemporal chaos in a discrete predator-prey system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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