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Time delay can enhance spatio-temporal chaos in a prey-predator model
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2016 (English)In: Ecological Complexity: An International Journal on Biocomplexity in the Environment and Theoretical Ecology, ISSN 1476-945X, E-ISSN 1476-9840, Vol. 27, 17-28 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we explore how the time delay induced Hopf-bifurcation interacts with Turing instability to determine the resulting spatial patterns. For this study, we consider a delayed prey-predator model with Holling type-II functional response and intra-specific competition among the predators. Analytical criteria for the delay induced Hopf-bifurcation and for the delayed spatio-temporal model are provided with numerical example to validate the analytical results. Exhaustive numerical simulation reveals the appearance of three types of stationary patterns, cold spot, labyrinthine, mixture of stripe-spot and two non-stationary patterns, quasi-periodic and spatio-temporal chaotic patterns. The qualitative features of the patterns for the non-delayed and the delayed spatio-temporal model are the same but their occurrence is solely controlled by the temporal parameters, rate of diffusivity and magnitude of the time delay. It is evident that the magnitude of time delay parameter beyond the Hopf-bifurcation threshold mostly produces spatio-temporal chaotic patterns. 

Place, publisher, year, edition, pages
2016. Vol. 27, 17-28 p.
Keyword [en]
Hutchinson's delay, Hopf-bifurcation, Turing instability, Spatial pattern, Chaos
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-127969DOI: 10.1016/j.ecocom.2015.12.001ISI: 000384386600004OAI: oai:DiVA.org:umu-127969DiVA: diva2:1055724
Available from: 2016-12-13 Created: 2016-11-21 Last updated: 2016-12-13Bibliographically approved

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Zhang, Lai
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Citation style
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