Global stability and bifurcation analysis of a harvested stage structure predator-prey system with linear functional response
Joint Authors
al-Umari, G. F. M.
al-Umari, S. K. Q.
Source
Jordan Journal of Mathematics and Statistics
Issue
Vol. 4, Issue 1 (30 Apr. 2011), pp.7-31, 25 p.
Publisher
Yarmouk University Deanship of Research and Graduate Studies
Publication Date
2011-04-30
Country of Publication
Jordan
No. of Pages
25
Main Subjects
Topics
Abstract EN
The global properties of a harvested stage-structured predator-prey model with linear functional response and constant delay are studied using Lyapunov functions and LaSalle’s invariance principle.
It is shown that time delay and the harvesting effort can cause a stable equilibrium to become unstable.
A condition which leads to the extinction of the predators is indicated.
We show also, that the predator coexists with prey permanently if and only if the predator’s recruitment rate at the peak of prey abundance is larger than its harvesting rate.
By choosing the delay as a bifurcation parameter, we show both analytically and numerically that Hopf bifurcation can occur as the delay crosses some critical value.
We, also present results on positivity and roundedness of the solution.
American Psychological Association (APA)
al-Umari, G. F. M.& al-Umari, S. K. Q.. 2011. Global stability and bifurcation analysis of a harvested stage structure predator-prey system with linear functional response. Jordan Journal of Mathematics and Statistics،Vol. 4, no. 1, pp.7-31.
https://search.emarefa.net/detail/BIM-266401
Modern Language Association (MLA)
al-Umari, G. F. M.& al-Umari, S. K. Q.. Global stability and bifurcation analysis of a harvested stage structure predator-prey system with linear functional response. Jordan Journal of Mathematics and Statistics Vol. 4, no. 1 (Apr. 2011), pp.7-31.
https://search.emarefa.net/detail/BIM-266401
American Medical Association (AMA)
al-Umari, G. F. M.& al-Umari, S. K. Q.. Global stability and bifurcation analysis of a harvested stage structure predator-prey system with linear functional response. Jordan Journal of Mathematics and Statistics. 2011. Vol. 4, no. 1, pp.7-31.
https://search.emarefa.net/detail/BIM-266401
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 30-31
Record ID
BIM-266401