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Three-dimensional pattern dynamics of a fractional predator-prey model with cross-diffusion and herd behavior

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

Abstract

In this paper, we study the pattern dynamics in a spatial fractional predator-prey model with cross fractional diffusion, herd behavior and prey refuge. In this model, herd behavior exists in the population of predators and the prey. The spatial dynamics of the system are obtained through appropriate threshold parameters, and a series of three-dimensional patterns are observed, such as tubes, planar lamellae and spherical droplets. Specifically, linear stability analysis is applied to obtain the conditions of Hopf bifurcation and Turing instability. Then, by utilizing the central manifold reduction theory analysis, the amplitude equation near the critical point of Turing bifurcation is deduced to study the selection and stability of pattern formation. The theoretical results are verified by numerical simulation.

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  • Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Three-dimensional pattern dynamics of a fractional predator-prey model with cross-diffusion and herd behavior," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000418
    DOI: 10.1016/j.amc.2022.126955
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    Cited by:

    1. Cao, Yan & Zhou, Wei-Jie & Liu, Xiao-Zhen & Wu, Kai-Ning, 2024. "Passivity of fractional reaction-diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    2. 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).

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