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2012 Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay
Xiaojian Zhou, Xin Chen, Yongzhong Song
J. Appl. Math. 2012: 1-15 (2012). DOI: 10.1155/2012/768364

Abstract

We investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis.

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Xiaojian Zhou. Xin Chen. Yongzhong Song. "Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay." J. Appl. Math. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/768364

Information

Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1264.91094
MathSciNet: MR3000283
Digital Object Identifier: 10.1155/2012/768364

Rights: Copyright © 2012 Hindawi

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