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Stability analysis and finite volume element discretization for delay-driven spatio-temporal patterns in a predator-prey model

机译:捕食-被捕食模型中时滞驱动时空模式的稳定性分析和有限体积离散

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Time delay is an essential ingredient of spatio-temporal predator-prey models since the reproduction of the predator population after predating the prey will not be instantaneous, but is mediated by a constant time lag accounting for the gestation of predators. In this paper we study a predator-prey reaction-diffusion system with time delay, where a stability analysis involving Hopf bifurcations with respect to the delay parameter and simulations produced by a new numerical method reveal how this delay affects the formation of spatial patterns in the distribution of the species. In particular, it turns out that when the carrying capacity of the prey is large and whenever the delay exceeds a critical value, the reaction-diffusion system admits a limit cycle due to the Hopf bifurcation. This limit cycle induces the spatio-temporal pattern. The proposed discretization consists of a finite volume element (FVE) method combined with a Runge-Kutta scheme.
机译:时间延迟是时空捕食者-捕食者模型的重要组成部分,因为捕食者在捕食者之后的繁殖不是瞬时的,而是由考虑到捕食者孕育的恒定时滞介导的。在本文中,我们研究了具有时滞的捕食者-食饵反应扩散系统,其中关于Hopf分支的时滞参数的稳定性分析和通过新的数值方法产生的模拟揭示了这种时延如何影响动物的空间格局的形成。物种分布。尤其是,事实证明,当猎物的承载能力大且延迟超过临界值时,由于霍普夫分支,反应扩散系统会进入极限循环。该极限周期引起时空模式。拟议的离散化方法由有限体积元素(FVE)方法与Runge-Kutta方案相结合组成。

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