Lotka-Volterra predator-prey model with periodically varying carrying capacity.
Lotka-Volterra predator-prey model with periodically varying carrying capacity.
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DOI：
10.1103/physreve.107.064144
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发表时间：
2022-11
期刊：
影响因子：
--
通讯作者：
M. Swailem;U. Täuber
中科院分区：
文献类型：
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作者：
M. Swailem;U. Täuber
研究了具有周期性变化的捕食者-食饵相互作用的随机空间Lotka-Volterra模型。描述被捕食种群有限食物资源的Lotka-Volterra模型具有连续的主动-吸收相变.活跃期是以追逐和躲避波的形式存在的时空模式所支持的。利用二维格子上的蒙特卡罗模拟研究了环境的季节变化对物种共存的影响。我们的模拟结果也与平均场分析进行了比较，以便具体描述随机波动和空间相关性的影响。我们发现当捕食者与被捕食者共存的容量周期性变化时，捕食者与被捕食者共存的参数范围相对于平稳情况是扩大的。周期变化的Lotka-Volterra捕食者-食饵系统的(准)定常状态在随机模型和平均场近似之间显示出定性的一致性。然而，在周期性的承载能力切换环境下，平均场速率方程预测了被随机格子模型中的内部反应噪声冲刷掉的周期倍增场景。利用格子模拟和动态关联函数的可视化表示，我们研究了追赶波和躲避波如何受到随后的共振效应的影响。相关函数测量表明，系统对环境突然变化的响应存在时间延迟。在我们的模拟中观察到了导致持久空间关联的共振特征。在快周期切换和慢周期切换的极端极限下，探索了不同的有效静态环境。通过对快切换区平均场方程的分析，可以半定量地描述(准)定态。
We study the stochastic spatial Lotka-Volterra model for predator-prey interaction subject to a periodically varying carrying capacity. The Lotka-Volterra model with on-site lattice occupation restrictions (i.e., finite local carrying capacity) that represent finite food resources for the prey population exhibits a continuous active-to-absorbing phase transition. The active phase is sustained by the existence of spatiotemporal patterns in the form of pursuit and evasion waves. Monte Carlo simulations on a two-dimensional lattice are utilized to investigate the effect of seasonal variations of the environment on species coexistence. The results of our simulations are also compared to a mean-field analysis in order to specifically delineate the impact of stochastic fluctuations and spatial correlations. We find that the parameter region of predator and prey coexistence is enlarged relative to the stationary situation when the carrying capacity varies periodically. The (quasi-)stationary regime of our periodically varying Lotka-Volterra predator-prey system shows qualitative agreement between the stochastic model and the mean-field approximation. However, under periodic carrying capacity-switching environments, the mean-field rate equations predict period-doubling scenarios that are washed out by internal reaction noise in the stochastic lattice model. Utilizing visual representations of the lattice simulations and dynamical correlation functions, we study how the pursuit and evasion waves are affected by ensuing resonance effects. Correlation function measurements indicate a time delay in the response of the system to sudden changes in the environment. Resonance features are observed in our simulations that cause prolonged persistent spatial correlations. Different effective static environments are explored in the extreme limits of fast and slow periodic switching. The analysis of the mean-field equations in the fast-switching regime enables a semiquantitative description of the (quasi-)stationary state.