The Dynamics of a Predator-Prey System with State-Dependent Feedback Control

Hunki Baek

Abstract and Applied Analysis, 2012, vol. 2012, 1-17

Abstract:

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.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2012/101386.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2012/101386.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:101386

DOI: 10.1155/2012/101386

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().