This work deals with a reaction-diffusion model for prey-predator interaction with Bazykin’s reaction kinetics and a nonlocal interaction term in prey growth. The kernel of the integral characterizes nonlocal consumption of resources and depends on space and time. Linear stability analysis determines the conditions of the emergence of Turing patterns without and with nonlocal term, while weakly nonlinear analysis allows the derivation of amplitude equations. The bifurcation analysis and numerical simulation carried out in this work reveal the existence of stationary and dynamic patterns appearing due to the loss of stability of the coexistence homogeneous steady-state.

中文翻译：

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时空非局部性的时空Bazykin模型

这项工作涉及一个反应扩散模型，该模型具有Bazykin的反应动力学和猎物生长中的非局部相互作用项，与猎物-捕食者相互作用。积分的内核表征了非本地资源消耗，并取决于空间和时间。线性稳定性分析确定了不带非局部项和带非局部项的图灵模式出现的条件，而弱非线性分析则允许推导振幅方程。在这项工作中进行的分叉分析和数值模拟表明，由于共存均匀稳态的稳定性损失，出现了平稳和动态模式。