<p>This paper proposes a reaction-diffusion system with time delay and nonlocal perception via a top-hat kernel for controlling Pine Wilt Disease. We analyze the existence conditions of Turing, Hopf, and Turing-Hopf bifurcations. By selecting appropriate parameters, we conduct numerical simulations. The simulation results indicate that the nonlocal perception can induce stable spatially inhomogeneous solutions. The time delay can induce stable spatially inhomogeneous periodic solutions. The nonlocal perception and time delay can jointly induce Turing-Hopf bifurcation, exhibiting rich dynamical phenomena near the bifurcation points. Small perturbations can lead to transitions between different spatiotemporal patterns, such as locally asymptotically stable solutions, stable spatially inhomogeneous solutions, and stable spatially inhomogeneous periodic solutions. Finally, we interpret the simulated phenomena and propose practical recommendations for Pine Wilt Disease control, thereby offering practical guidance for real-world prevention and management efforts.</p>

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Spatiotemporal patterns induced by nonlocal perception and time delay in a Pine Wilt Disease model

  • Jie Yang,
  • Yujuan Gao,
  • Yuting Ding

摘要

This paper proposes a reaction-diffusion system with time delay and nonlocal perception via a top-hat kernel for controlling Pine Wilt Disease. We analyze the existence conditions of Turing, Hopf, and Turing-Hopf bifurcations. By selecting appropriate parameters, we conduct numerical simulations. The simulation results indicate that the nonlocal perception can induce stable spatially inhomogeneous solutions. The time delay can induce stable spatially inhomogeneous periodic solutions. The nonlocal perception and time delay can jointly induce Turing-Hopf bifurcation, exhibiting rich dynamical phenomena near the bifurcation points. Small perturbations can lead to transitions between different spatiotemporal patterns, such as locally asymptotically stable solutions, stable spatially inhomogeneous solutions, and stable spatially inhomogeneous periodic solutions. Finally, we interpret the simulated phenomena and propose practical recommendations for Pine Wilt Disease control, thereby offering practical guidance for real-world prevention and management efforts.