The Dynamics of a Predator-Prey System with State-Dependent Feedback Control
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-13
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
A Lotka-Volterra-type predator-prey system with state-dependent feedback control is investigated in both theoretical and numerical ways.
Using the Poincaré map and the analogue of the Poincaré criterion, the sufficient conditions for the existence and stability of semitrivial periodic solutions and positive periodic solutions are obtained.
In addition, we show that there is no positive periodic solution with period greater than and equal to three under some conditions.
The qualitative analysis shows that the positive period-one solution bifurcates from the semitrivial solution through a fold bifurcation.
Numerical simulations to substantiate our theoretical results are provided.
Also, the bifurcation diagrams of solutions are illustrated by using the Poincaré map, and it is shown that the chaotic solutions take place via a cascade of period-doubling bifurcations.
American Psychological Association (APA)
Baek, Hunki. 2012. The Dynamics of a Predator-Prey System with State-Dependent Feedback Control. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-446368
Modern Language Association (MLA)
Baek, Hunki. The Dynamics of a Predator-Prey System with State-Dependent Feedback Control. Abstract and Applied Analysis No. 2012 (2012), pp.1-17.
https://search.emarefa.net/detail/BIM-446368
American Medical Association (AMA)
Baek, Hunki. The Dynamics of a Predator-Prey System with State-Dependent Feedback Control. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-446368
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-446368