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Influence of discrete delay on pattern formation in a ratio-dependent prey-predator model
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2014 (English)In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 67, 73-81 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we explore how the two mechanisms, Turing instability and Hopf bifurcation, interact to determine the formation of spatial patterns in a ratio-dependent prey predator model with discrete time delay. We conduct both rigorous analysis and extensive numerical simulations. Results show that four types of patterns, cold spot, labyrinthine, chaotic as well as mixture of spots and labyrinthine can be observed with and without time delay. However, in the absence of time delay, the two aforementioned mechanisms have a significant impact on the emergence of spatial patterns, whereas only Hopf bifurcation threshold is derived by considering the discrete time delay as the bifurcation parameter. Moreover, time delay promotes the emergence of spatial patterns via spatio-temporal Hopf bifurcation compared to the non-delayed counterpart, implying the destabilizing role of time delay. In addition, the destabilizing role is prominent when the magnitude of time delay and the ratio of diffusivity are comparatively large. 

Place, publisher, year, edition, pages
2014. Vol. 67, 73-81 p.
National Category
Mathematics Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-99977DOI: 10.1016/j.chaos.2014.06.012ISI: 000340982400008OAI: oai:DiVA.org:umu-99977DiVA: diva2:789006
Available from: 2015-02-17 Created: 2015-02-17 Last updated: 2017-12-04Bibliographically approved

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Zhang, Lai

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