Extinction and Permanence of a General Predator-Prey System with Impulsive Perturbations
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-08-14
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
A general predator-prey system is studied in a scheme where there is periodic impulsive perturbations.
This scheme has the potential to protect the predator from extinction but under some conditions may also serve to lead to extinction of the prey.
Conditions for extinction and permanence are obtained via the comparison methods involving monotone theory of impulsive systems and multiple Liapunov functions, which establish explicit bounds on solutions.
The existence of a positive periodic solution is also studied by the bifurcation theory.
Application is given to a Lotka-Volterra predator-prey system with periodic impulsive immigration of the predator.
It is shown that the results are quite different from the corresponding system without impulsive immigration, where extinction of the prey can never be achieved.
The prey will be extinct or permanent independent of whether the system without impulsive effect immigration is permanent or not.
The model and its results suggest an approach of pest control which proves more effective than the classical one.
American Psychological Association (APA)
Liu, Xianning& Chen, Lansun. 2012. Extinction and Permanence of a General Predator-Prey System with Impulsive Perturbations. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-993335
Modern Language Association (MLA)
Liu, Xianning& Chen, Lansun. Extinction and Permanence of a General Predator-Prey System with Impulsive Perturbations. Journal of Applied Mathematics No. 2012 (2012), pp.1-19.
https://search.emarefa.net/detail/BIM-993335
American Medical Association (AMA)
Liu, Xianning& Chen, Lansun. Extinction and Permanence of a General Predator-Prey System with Impulsive Perturbations. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-993335
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993335