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Hopf bifurcation analysis of a food-limited population model with delay

✍ Scribed by Aying Wan; Junjie Wei

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 707 KB
Volume: 11
Category: Article
ISSN: 1468-1218
DOI: 10.1016/j.nonrwa.2009.01.052

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✦ Synopsis

The dynamics of a food-limited population model with delay are investigated. We prove that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived, using the theory of normal form and center manifold. Global existence of periodic solutions is established by using a global Hopf bifurcation result due to [J. Wu, Symmetric functional differential equations and neural networks with memory, Trans. Amer. Math. Soc. 350 (1998) 4799-4838].

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