Pattern formation of a predator–prey system with Ivlev-type functional response

Weiming Wang, Lei Zhang, Hailing Wang and Zhenqing Li

Ecological Modelling, 2010, vol. 221, issue 2, 131-140

Abstract: In this paper, we investigate the spatial pattern formation of a predator–prey system with prey-dependent functional response Ivlev-type and reaction-diffusion. The Hopf bifurcation of the model is discussed, and the sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained. Based on this, we perform the spiral and the chaotic spiral patterns via numerical simulation, i.e., the evolution process of the system with the initial conditions which was small amplitude random perturbation around the steady state. For the sake of learning the pattern formation of the model further, we perform three categories of unsymmetric initial condition, and find that with these special initial conditions the system can emerge not only spiral pattern but also target pattern and so on, and the effect of these special conditions on the formation of spatial patterns is less and less with more and more iterations but the effect does not decay forever. This indicates that for prey-dependent type predator–prey system, pattern formations do depend on the initial conditions, while for predator-dependent type they do not.

Keywords: Hopf bifurcation; Turing instability; Spatiotemporal pattern; Spiral; Target (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304380009006310
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:221:y:2010:i:2:p:131-140

DOI: 10.1016/j.ecolmodel.2009.09.011

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 ().