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

Discrete Dynamics in Nature and Society

Volumn 2011, Issue , 2011, Pages

  Khoshsiar Ghaziani, R ^a   Govaerts, W ^b   Sonck, C ^b  

^a SHAHREKORD UNIVERSITY   (Iran)

^b GHENT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80052652287     PISSN: 10260226     EISSN: 1607887X     Source Type: Journal    
DOI: 10.1155/2011/862494     Document Type: Article

References (19)

1. Berryman A. A., The origins and evolution of predator-prey theory Ecology 1992 73 5 1530 1535 (Pubitemid 23397216)
2. Fan M., Wang K., Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system Mathematical and Computer Modelling 2002 35 9-10 951 961 (Pubitemid 40047416)
3. Fang H., Cao J. D., Global existence for positive periodic solutions to a class of predator-prey systems Journal of Biomathematics 2000 15 4 403 407
4. Freedman H. I., Deterministic Mathematical Models in Population Ecology 1980 57 New York, NY, USA Marcel Dekker x+254 Monographs and Textbooks in Pure and Applied Mathematics
5. Goh B. S., Management and Analysis of Biological Populations 1980 Amsterdam, The Netherlands Elsevier
6. Murray J. D., Mathematical Biology 1993 19 2nd Berlin, Germany Springer xiv+767 Biomathematics
7. Bazykin A. D., Nonlinear Dynamics of Interacting Populations 1998 11 River Edge, NJ, USA World Scientific xxii+193 World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, A. I. Khibnik and B. Krauskopf, Eds.
8. Arnold V. I., Geometrical Methods in the Theory of Ordinary Differential Equations 1983 250 New York, NY, USA Springer xi+334 Grundlehren der Mathematischen Wissenschaften
9. Kuznetsov Y. A., Elements of Applied Bifurcation Theory 2004 112 3rd New York, NY, USA Springer xxii+631 Applied Mathematical Sciences
10. Broer H. W., Saleh K., Naudot V., Roussarie R., Dynamics of a predator-prey model with non-monotonic response function Discrete and Continuous Dynamical Systems. Series A 2007 18 2-3 221 251
11. Doedel E. J., Champneys R. A., Fairgrieve T. F., Kuznetsov Yu. A., Sandstede B., Wang X. J., AUTO2000: Continuation and Bifurcation Sotware for Ordinary Differential Equations (with HomCont), Users Guide. Concordia University, Montreal, Canada 19972000, http://indy.cs.concordia.ca
12. Govaerts W., Kuznetsov Yu. A., Matcont: a Matlab software project for the numerical continuation and bifurcation study of continuous and discrete parameterized dynamical systems. http://sourceforge.net/
13. Agarwal R. P., Difference Equations and Inequalities: Theory, Methods, and Applicationa 2000 228 2nd New York, NY, USA Marcel Dekker xvi+971 Monographs and Textbooks in Pure and Applied Mathematics
14. Govaerts W., Ghaziani R. K., Kuznetsov Yu. A., Meijer H. G. E., Numerical methods for two-parameter local bifurcation analysis of maps SIAM Journal on Scientific Computing 2007 29 6 2644 2667
15. Danca M., Codreanu S., Bak B., Detailed analysis of a nonlinear prey-predator model Journal of Biological Physics 1997 23 1 11 20 (Pubitemid 127509066)
16. Murakami K., Stability and bifurcation in a discrete-time predator-prey model Journal of Difference Equations and Applications 2007 13 10 911 925
17. Li S., Zhang W., Bifurcations of a discrete prey-predator model with Holling type II functional response Discrete and Continuous Dynamical Systems. Series B 2010 14 1 159 176
18. Allgower E. L., Georg K., Numerical Continuation Methods: An Introduction 1990 13 Berlin, Germany Springer xiv+388 Springer Series in Computational Mathematics
19. Kraft R. L., Chaos, Cantor sets, and hyperbolicity for the logistic maps The American Mathematical Monthly 1999 106 5 400 408