Bifurcation analysis of an agent-based model for predator–prey interactions

C. Colon, D. Claessen and M. Ghil

Ecological Modelling, 2015, vol. 317, issue C, 93-106

Abstract: 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.

Keywords: ODE; Hopf bifurcation; Heteroclinic bifurcation; Time series analysis; Singular spectrum analysis; Critical transition; Early-warning signals (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304380015004111
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ecomod:v:317:y:2015:i:c:p:93-106

DOI: 10.1016/j.ecolmodel.2015.09.004

Access Statistics for this article

Ecological Modelling is currently edited by Brian D. Fath

More articles in Ecological Modelling from Elsevier
Bibliographic data for series maintained by Catherine Liu ().