Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system

Tousheng Huang and Huayong Zhang

Chaos, Solitons & Fractals, 2016, vol. 91, issue C, 92-107

Abstract: The spatiotemporal dynamics of a space- and time-discrete predator–prey system is investigated in this research. The conditions for stable homogeneous stationary state of the system are derived via stability analysis. By using center manifold theorem and bifurcation theory, critical parameter values for flip bifurcation, Hopf bifurcation and Turing bifurcation are determined, respectively. Based on the bifurcation analysis, pattern formation conditions are also provided. Numerical simulations are performed not only to illustrate the theoretical results, but also to exhibit new and complex dynamical behaviors, including period-doubling cascade, invariant circles, periodic windows, chaotic dynamics, and pattern formation. Maximum Lyapunov exponents are calculated to distinguish chaos from regular behaviors. In the routes from bifurcation to chaos, flip-Turing instability and Hopf-Turing instability emerge, capturing the formation of diverse complex patterns, such as mosaic, circle, spiral, spatiotemporal chaotic patterns, and so on. The analysis and results in this research contribute to a new understanding on the relationship among bifurcation, chaos and pattern formation.

Keywords: Flip bifurcation; Hopf bifurcation; Turing bifurcation; Pattern formation; Chaos; Predator–prey system (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077916301771
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:91:y:2016:i:c:p:92-107

DOI: 10.1016/j.chaos.2016.05.009

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. ().