Multiple positive periodic solutions of a delayed discrete predator-prey system with type IV functional responses

Applied Mathematics Letters

Volumn 20, Issue 10, 2007, Pages 1031-1038

  Zhang, Weipeng ^a   Zhu, Deming ^a   Bi, Ping ^a  

^a EAST CHINA NORMAL UNIVERSITY   (China)

Author keywords

Coincidence degree; Difference equations; Positive periodic solution; Predator prey systems; Type IV functional response

Indexed keywords

DIFFERENCE EQUATIONS; ECOLOGY; PROBLEM SOLVING; THEOREM PROVING;

COINCIDENCE DEGREE; POSITIVE PERIODIC SOLUTION; PREDATOR-PREY SYSTEMS; TYPE IV FUNCTIONAL RESPONSE;

LIVING SYSTEMS STUDIES;

EID: 34547578466     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2006.11.005     Document Type: Article

References (18)

1. Agarwal R.P. Difference Equations and Inequalities: Theory, Methods and Applications. Monographs and Textbooks in Pure and Applied Mathematics vol. 228 (2000), Marcel Dekker Inc., New York
2. Arditi R., Perrin N., and Saiah H. Functional response and heterogeneities: An experimental test with cladocerans. OIKOS 60 (1991) 69-75
3. Berryman A.A. The origins and evolution of predator-prey theory. Ecology 75 (1992) 1530-1535
4. Chen Y.M. Multiple periodic solutions of delayed predator-prey systems with type IV functional responses. Nonlinear Anal. 5 (2004) 45-53
5. Fan M., and Wang K. Periodic solutions of a discrete time non-autonomous ratio-dependent predator-prey system. Math. Comput. Modelling 35 (2002) 951-961
6. Freedman H.I. Deterministic Mathematical Models in Population Ecology (1980), Marcel Dekker, New York
7. Gaines R.E., and Mawhin J.L. Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag, Berlin
8. Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics (1992), Kluwer Academic, Boston
9. Hanski I. The functional response of predator: Worries about scale. TREE 6 (1991) 141-142
10. Holling C.S. The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Ent. Soc. Can. 45 (1965) 1-60
11. Maynard S.J. Models in Ecology (1974), Cambridge University Press, Cambridge
12. May R.M. Stability and Complexity in Model Ecosystems (1974), Princeton University Press
13. Murry J.D. Mathematical Biology (1989), Springer-Verlag, New York
14. Rosenzweig M.L., and MacArthur R.H. Graphical representation and stability conditions of predator-prey interactions. Amer. Nat. 47 (1963) 209-223
15. Rosenzweig M.L. Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time. Science 171 (1969) 385-387
16. Xu R., Chaplain M.A.J., and Davidson F.A. Periodic solutions for a predator-prey model with Holling-type functional response and time delays. Appl. Math. Comput. 161 (2005) 637-654
17. Wang L.L., and Li W.T. Existence and global stability of positive periodic solutions of a predator-prey system with delays. Appl. Math. Comput. 146 (2004) 167-185
18. Wang L.L., and Li W.T. 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