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Hopf bifurcation analysis in a diffusive food-chain model with time delay
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2013 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, Vol. 66, no 10, 2139-2153 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider the direction and stability of time-delay induced Hopf bifurcation in a three species food-chain model with diffusion. By means of analyzing eigenvalue spectrum and Lyapunov functional, we show that the positive equilibrium is asymptotically stable in the absence of time delay, but loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold. Using the norm form and the center manifold theory, we investigate the stability and direction of the Hopf bifurcation. The instability of the Hopf bifurcation leads to the emergence of spatial patterns. Numerical calculations are performed to illustrate our theoretical results.

Place, publisher, year, edition, pages
Elsevier, 2013. Vol. 66, no 10, 2139-2153 p.
Keyword [en]
Food chain, Hopf bifurcation, Pattern formation, Time delay
National Category
URN: urn:nbn:se:umu:diva-83198DOI: 10.1016/j.camwa.2013.09.002OAI: diva2:669042
ICNC-FSKD 2012, 29–31 May 2012 in Chongqing, China. The joint International Conference on Natural Computation (ICNC) and on Fuzzy Systems and Knowledge Discovery (FSKD).
Available from: 2013-12-02 Created: 2013-11-21 Last updated: 2014-01-15Bibliographically approved

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Zhang, Lai
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