Journal of Applied Mathematics
Volume 2012 (2012), Article ID 768364, 15 pages
http://dx.doi.org/10.1155/2012/768364
Research Article

Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay

Xiaojian Zhou,1,2 Xin Chen,1 and Yongzhong Song1

1Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
2School of Science, Nantong University, Nantong 226008, China

Received 7 September 2012; Accepted 26 September 2012

Academic Editor: Junjie Wei

Copyright © 2012 Xiaojian Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.