Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays
Joint Authors
Zhang, Xue
Xiang, Zhongyi
Zhang, Qing-ling
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-10
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Zhang, Xue& Zhang, Qing-ling& Xiang, Zhongyi. 2014. Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1014708
Modern Language Association (MLA)
Zhang, Xue…[et al.]. Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays. Abstract and Applied Analysis No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-1014708
American Medical Association (AMA)
Zhang, Xue& Zhang, Qing-ling& Xiang, Zhongyi. Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1014708
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014708