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Memory-based movement with spatiotemporal distributed delays in diffusion and reaction

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  • Song, Yongli
  • Wu, Shuhao
  • Wang, Hao

Abstract

In this paper, we investigate the spatiotemporal dynamics of a single-species model with spatiotemporal delays characterizing spatial memory and maturation. Through stability and bifurcation analysis, we find that the spatial memory-based diffusion coefficient, the spatiotemporal diffusive delay and spatiotemporal reaction delay have important effects on the dynamics of the model and their combined impact can cause the destabilization of the positive constant steady state and give rise to steady state and Hopf bifurcations. Taking the coefficient of spatial memory diffusion as the bifurcation parameter, the critical values of steady state and Hopf bifurcations are rigorously determined. Furthermore, we apply the theoretical results to a modified diffusive logistic model with predation and obtain spatially inhomogeneous steady states and spatially homogeneous and inhomogeneous periodic solutions via numerical simulations.

Suggested Citation

  • Song, Yongli & Wu, Shuhao & Wang, Hao, 2021. "Memory-based movement with spatiotemporal distributed delays in diffusion and reaction," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    • Handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321003441
    DOI: 10.1016/j.amc.2021.126254
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    Cited by:

    1. Ye, Luhong & Zhao, Hongyong & Wu, Daiyong, 2023. "Spatial movement with memory-induced cross-diffusion effect and toxin effect in predator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 68-91.
    2. Lv, Yehu, 2022. "The spatially homogeneous hopf bifurcation induced jointly by memory and general delays in a diffusive system," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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