Codimension-Two Bifurcations of Fixed Points in a Class of Discrete Prey-Predator Systems
Joint Authors
Khoshsiar Ghaziani, R.
Sonck, C.
Govaerts, W.
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-27, 27 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-06-09
Country of Publication
Egypt
No. of Pages
27
Main Subjects
Abstract EN
The dynamic behaviour of a Lotka-Volterra system, described by a planar map, is analytically and numerically investigated.
We derive analytical conditions for stability and bifurcation of the fixed points of the system and compute analytically the normal form coefficients for the codimension 1 bifurcation points (flip and Neimark-Sacker), and so establish sub- or supercriticality of these bifurcation points.
Furthermore, by using numerical continuation methods, we compute bifurcation curves of fixed points and cycles with periods up to 16 under variation of one and two parameters, and compute all codimension 1 and codimension 2 bifurcations on the corresponding curves.
For the bifurcation points, we compute the corresponding normal form coefficients.
These quantities enable us to compute curves of codimension 1 bifurcations that branch off from the detected codimension 2 bifurcation points.
These curves form stability boundaries of various types of cycles which emerge around codimension 1 and 2 bifurcation points.
Numerical simulations confirm our results and reveal further complex dynamical behaviours.
American Psychological Association (APA)
Khoshsiar Ghaziani, R.& Govaerts, W.& Sonck, C.. 2011. Codimension-Two Bifurcations of Fixed Points in a Class of Discrete Prey-Predator Systems. Discrete Dynamics in Nature and Society،Vol. 2011, no. 2011, pp.1-27.
https://search.emarefa.net/detail/BIM-504279
Modern Language Association (MLA)
Khoshsiar Ghaziani, R.…[et al.]. Codimension-Two Bifurcations of Fixed Points in a Class of Discrete Prey-Predator Systems. Discrete Dynamics in Nature and Society No. 2011 (2011), pp.1-27.
https://search.emarefa.net/detail/BIM-504279
American Medical Association (AMA)
Khoshsiar Ghaziani, R.& Govaerts, W.& Sonck, C.. Codimension-Two Bifurcations of Fixed Points in a Class of Discrete Prey-Predator Systems. Discrete Dynamics in Nature and Society. 2011. Vol. 2011, no. 2011, pp.1-27.
https://search.emarefa.net/detail/BIM-504279
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-504279