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Mathematical Problems in Engineering
Volume 2014, Article ID 535634, 8 pages
Research Article

Stability and Bifurcation Analysis of a Singular Delayed Predator-Prey Bioeconomic Model with Stochastic Fluctuations

Institute of Systems Science, Northeastern University, Shenyang 110819, China

Received 25 August 2014; Accepted 25 November 2014; Published 7 December 2014

Academic Editor: Hongyong Zhao

Copyright © 2014 Yue Zhang and Qingling Zhang. 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.


This study investigates a singular delayed predator-prey bioeconomic model with stochastic fluctuations, which is described by differential-algebraic equations because of economic factors. The interior equilibrium of the singular delayed predator-prey bioeconomic model switches from being stable to unstable and then back to being stable, with the increase in time delay. The critical values for stability switches and Hopf bifurcations can be analytically determined. Subsequently, the effect of a fluctuating environment on the singular stochastic delayed predator-prey bioeconomic model obtained by introducing Gaussian white noise terms to the aforementioned deterministic model system is discussed. The fluctuation intensity of the population and harvest effort are calculated by Fourier transform method. Numerical simulation results are presented to verify the effectiveness of the conclusions.