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2014 Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays
Xue Zhang, Qing-ling Zhang, Zhongyi Xiang
Abstr. Appl. Anal. 2014: 1-12 (2014). DOI: 10.1155/2014/745296


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.


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Xue Zhang. Qing-ling Zhang. Zhongyi Xiang. "Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays." Abstr. Appl. Anal. 2014 1 - 12, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022999
MathSciNet: MR3182303
Digital Object Identifier: 10.1155/2014/745296

Rights: Copyright © 2014 Hindawi


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