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Codimension-two bifurcations of fixed points in a class of discrete prey-predator systems

Reza Khoshsiar Ghaziani, Willy Govaerts UGent and Charlotte Sonck UGent (2011) DISCRETE DYNAMICS IN NATURE AND SOCIETY.
abstract
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
MODEL, MAPS
journal title
DISCRETE DYNAMICS IN NATURE AND SOCIETY
Discrete Dyn. Nat. Soc.
article_number
862494
pages
24 pages
Web of Science type
Article
Web of Science id
000293569200001
JCR category
MULTIDISCIPLINARY SCIENCES
JCR impact factor
0.688 (2011)
JCR rank
24/54 (2011)
JCR quartile
2 (2011)
ISSN
1026-0226
DOI
10.1155/2011/862494
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1894259
handle
http://hdl.handle.net/1854/LU-1894259
date created
2011-08-29 16:06:20
date last changed
2011-08-30 09:05:09
@article{1894259,
  abstract     = {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.},
  articleno    = {862494},
  author       = {Khoshsiar Ghaziani, Reza and Govaerts, Willy and Sonck, Charlotte},
  issn         = {1026-0226},
  journal      = {DISCRETE DYNAMICS IN NATURE AND SOCIETY},
  keyword      = {MODEL,MAPS},
  language     = {eng},
  pages        = {24},
  title        = {Codimension-two bifurcations of fixed points in a class of discrete prey-predator systems},
  url          = {http://dx.doi.org/10.1155/2011/862494},
  year         = {2011},
}

Chicago
Khoshsiar Ghaziani, Reza, Willy Govaerts, and Charlotte Sonck. 2011. “Codimension-two Bifurcations of Fixed Points in a Class of Discrete Prey-predator Systems.” Discrete Dynamics in Nature and Society.
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.
Vancouver
1.
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;
MLA
Khoshsiar Ghaziani, Reza, Willy Govaerts, and Charlotte Sonck. “Codimension-two Bifurcations of Fixed Points in a Class of Discrete Prey-predator Systems.” DISCRETE DYNAMICS IN NATURE AND SOCIETY (2011): n. pag. Print.