Complex dynamic behaviors of a discrete-time predator–prey system

Xiaoli Liu and Dongmei Xiao

Chaos, Solitons & Fractals, 2007, vol. 32, issue 1, 80-94

Abstract: The dynamics of a discrete-time predator–prey system is investigated in the closed first quadrant R+2. It is shown that the system undergoes flip bifurcation and Hopf bifurcation in the interior of R+2 by using center manifold theorem and bifurcation theory. Numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors, such as the period-5, 6, 9, 10, 14, 18, 20, 25 orbits, cascade of period-doubling bifurcation in period-2, 4, 8, quasi-periodic orbits and the chaotic sets. These results reveal far richer dynamics of the discrete model compared with the continuous model. The Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors.

Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (30)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077905010325
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:chsofr:v:32:y:2007:i:1:p:80-94

DOI: 10.1016/j.chaos.2005.10.081

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().