Abstract and Applied Analysis

Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays

Xue Zhang, Qing-ling Zhang, and Zhongyi Xiang

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Abstract

A singular prey-predator model with time delays is formulated and analyzed. Allee effect is considered on the growth of the prey population. The singular prey-predator model is transformed into its normal form by using differential-algebraic system theory. We study its dynamics in terms of local analysis and Hopf bifurcation. The existence of periodic solutions via Hopf bifurcation with respect to two delays is established. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold argument. Finally, numerical simulations are included supporting the theoretical analysis and displaying the complex dynamical behavior of the model outside the domain of stability.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 745296, 12 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273233

Digital Object Identifier
doi:10.1155/2014/745296

Mathematical Reviews number (MathSciNet)
MR3182303

Zentralblatt MATH identifier
07022999

Citation

Zhang, Xue; Zhang, Qing-ling; Xiang, Zhongyi. Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays. Abstr. Appl. Anal. 2014 (2014), Article ID 745296, 12 pages. doi:10.1155/2014/745296. https://projecteuclid.org/euclid.aaa/1412273233


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