Direction and Stability of Bifurcating Periodic Solutions in a Delay-Induced Ecoepidemiological System
Author
Source
International Journal of Differential Equations
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-25, 25 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-11-02
Country of Publication
Egypt
No. of Pages
25
Main Subjects
Abstract EN
A SI-type ecoepidemiological model that incorporates reproduction delay of predator is studied.
Considering delay as parameter, we investigate the effect of delay on the stability of the coexisting equilibrium.
It is observed that there is stability switches, and Hopf bifurcation occurs when the delay crosses some critical value.
By applying the normal form theory and the center manifold theorem, the explicit formulae which determine the stability and direction of the bifurcating periodic solutions are determined.
Computer simulations have been carried out to illustrate different analytical findings.
Results indicate that the Hopf bifurcation is supercritical and the bifurcating periodic solution is stable for the considered parameter values.
It is also observed that the quantitative level of abundance of system populations depends crucially on the delay parameter if the reproduction period of predator exceeds the critical value.
American Psychological Association (APA)
Bairagi, N.. 2011. Direction and Stability of Bifurcating Periodic Solutions in a Delay-Induced Ecoepidemiological System. International Journal of Differential Equations،Vol. 2011, no. 2011, pp.1-25.
https://search.emarefa.net/detail/BIM-513037
Modern Language Association (MLA)
Bairagi, N.. Direction and Stability of Bifurcating Periodic Solutions in a Delay-Induced Ecoepidemiological System. International Journal of Differential Equations No. 2011 (2011), pp.1-25.
https://search.emarefa.net/detail/BIM-513037
American Medical Association (AMA)
Bairagi, N.. Direction and Stability of Bifurcating Periodic Solutions in a Delay-Induced Ecoepidemiological System. International Journal of Differential Equations. 2011. Vol. 2011, no. 2011, pp.1-25.
https://search.emarefa.net/detail/BIM-513037
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-513037