Multiple bifurcations in a predator-prey system with monotonic functional response

Applied Mathematics and Computation

Volumn 172, Issue 2 SPEC. ISS., 2006, Pages 1103-1120

  Wang, Lin Lin ^a   Fan, Yong Hong ^a   Li, Wan Tong ^b  

^a TIANJIN UNIVERSITY   (China)

^b LANZHOU UNIVERSITY   (China)

Author keywords

Bogdanov Takens bifurcation; Predator prey system; Qualitative analysis; Saddle node Bifurcation

Indexed keywords

DYNAMICS; FUNCTIONS; MATHEMATICAL MODELS; PARAMETER ESTIMATION;

PREDATOR-PREY SYSTEMS; SADDLE-NODE BIFURCATION;

BIFURCATION (MATHEMATICS);

EID: 31644446271     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.03.010     Document Type: Conference Paper

References (23)

1. A.A. Berryman The origins and evolution of predator-prey theory Ecology 73 1992 1530 1535
2. R. Bogdanov Bifurcations of a limit cycle for a family of vector fields on the plan Selecta Math. Soviet. 1 1981 373 388
3. R. Bogdanov Versal deformations of a singular point on the plan in the case of zero eigen-values Selecta Math. Soviet. 1 1981 389 421
4. J.P. Chen, and H.D. Zhang The qualitative analysis of two species predator-prey model with Holling's type III functional response Appl. Math. Mech. 7 1 1986 73 80
5. S.N. Chow, and J.K. Hale Methods of Bifurcation Theory 1982 Springer-Verlag New York, Heidelberg, Berlin
6. S.N. Chow, C.Z. Li, and D. Wang Normal Forms and Bifurcation of Planar Vector Fields 1994 Cambridge University Press Cambridge
7. H.I. Freedman Deterministic Mathematical Models in Population Ecology 1980 Marcel Dekker New York
8. M. Hesaaraki, and S.M. Moghadas Nonexistence of limit cycles in a predator-prey system with a sigmoid functional response Cana. Appl. Math. Quar. 7 4 1999 1 8
9. C.S. Holling The functional response of predator to prey density and its role in mimicry and population regulation Mem. Ent. Sec. Can. 45 1965 1 60
10. V.S. Ivlev Experimental Ecology of the Feeding of Fishes 1961 Yale University Press
11. N.D. Kazarinoff, and P. Van Den Driessche A model predator-prey system with functional response Math. Biosci. 39 1-2 1978 125 134
12. L.L. Wang, and W.T. Li Existence of periodic solutions of a delayed predator-prey system with functional response Int. J. Math. Sci. 1 2002 55 63
13. L.L. Wang, and W.T. Li Existence and global stability of positive periodic solutions of a predator-prey system with delays Appl. Math. Comput. 146 1 2003 167 185
14. L.L. Wang, and W.T. Li Periodic solutions and permanence for a delayed nonautonomous ratio-dependent predator-prey model with Holling type functional response J. Comput. Appl. Math. 162 2004 341 357
15. Y.A. Kuznetsov Elements of Applied Bifurcation Theory 1998 Springer-Verlag New York
16. R.M. May Complexity and Stability in Model Ecosystems 1973 Princeton University Press Princeton, NJ
17. J.D. Murry Mathematical Biology 1989 Springer-Verlag New York
18. M.R. Myerscough, M.J. Darwen, and W.L. Hogarth Stability, persistence and structural stability in a classical predator-prey model Ecol. Model. 89 1996 31 42
19. M.L. Rosenzweig Paradox of enrichment: destabilization of exploitation ecosystem in ecological time Science 171 1971 385 387
20. S. Ruan, and D. Xiao Global analysis in a predator-prey system with nonmonotonic functional response SIAM J. Appl. Math. 61 2001 1445 1472
21. S. Ruan, and W. Wang Dynamical behavior of an epidemic model with a nonlinear incidence rate J. Differen. Equat. 188 2003 135 163
22. D. Xiao, and S. Ruan Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response J. Differen. Equat. 176 2001 494 510
23. D. Xiao, and S. Ruan Bogdanov-Takens bifurcations in predator-prey systems with constant rate harvesting Fieids Institute Commun. 21 1999 493 506