Bifurcation analysis of an agent-based model for predator-prey interactions
Bifurcation analysis of an agent-based model for predator-prey interactions
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DOI：
10.1016/j.ecolmodel.2015.09.004
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发表时间：
2015-12-10
影响因子：
3.1
通讯作者：
Ghil, M.
中科院分区：
文献类型：
--
作者：
Colon, C.;Claessen, D.;Ghil, M.
Rosenzweig-MacArthur模型是一组常微分方程组(ODE)，它提供了捕食者-食饵系统动力学的综合描述。当食饵具有Allee效应时，该模型表现出双稳态，包括干叉分叉、Hopf分叉和异宿分叉。我们在二维正方形格子上开发了一个基于代理的模型(ABM)，它包含了聚集模型的关键假设。虽然ODE和ABM的两种建模方法不同，但这两种模型都显示出相似的分叉模式。ABM模型的行为更丰富，并使用先进的统计方法进行分析。特别是，奇异谱分析被用来稳健地定位在固定点周围明显随机的小幅度波动和稳定的大幅度振荡之间的过渡。模型轨迹的临界减速预示着异宿分叉。ABM和ODE模型的行为之间的系统比较有助于人们更好地理解捕食者-猎物系统；它为模型探索提供指导，并允许人们对捕食者-猎物相互作用的性质得出更可靠的结论。(C)2015爱思唯尔B.V.保留所有权利。
The Rosenzweig-MacArthur model is a set of ordinary differential equations (ODEs) that provides an aggregate description of the dynamics of a predator prey system. When including an Allee effect on the prey, this model exhibits bistability and contains a pitchfork bifurcation, a Hopf bifurcation and a heteroclinic bifurcation. We develop an agent-based model (ABM) on a two-dimensional, square lattice that encompasses the key assumptions of the aggregate model. Although the two modelling approaches ODE and ABM differ, both models exhibit similar bifurcation patterns. The ABM model's behaviour is richer and it is analysed using advanced statistical methods. In particular, singular spectrum analysis is used to robustly locate the transition between apparently random, small-amplitude fluctuations around a fixed point and stable, large-amplitude oscillations. Critical slowing down of model trajectories anticipates the heteroclinic bifurcation. Systematic comparison between the ABM and the ODE models' behaviour helps one understand the predator prey system better; it provides guidance in model exploration and allows one to draw more robust conclusions on the nature of predator prey interactions. (C) 2015 Elsevier B.V. All rights reserved.