Positive periodic solution for a semi-ratio-dependent predator-prey system with diffusion and time delays

Nonlinear Analysis: Real World Applications

Volumn 9, Issue 2, 2008, Pages 239-249

  Ding, Xiaoquan ^a   Wang, Fangfang ^a  

^a SHANDONG AGRICULTURAL UNIVERSITY   (China)

Author keywords

Coincidence degree; Diffusion; Periodic solution; Predator prey system; Semi ratio dependent

Indexed keywords

CONTINUOUS TIME SYSTEMS; NUMERICAL METHODS; PROBLEM SOLVING; THEOREM PROVING; TIME DELAY;

COINCIDENCE DEGREE; PERIODIC SOLUTIONS; PREDATOR-PREY SYSTEMS; SEMI-RATIO-DEPENDENT;

TIME VARYING SYSTEMS;

EID: 37249092975     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2006.09.011     Document Type: Article

References (22)

1. Beretta E., and Kuang Y. Global analysis in some delayed ratio-dependent predator-prey systems. Nonlinear Anal. TMA 32 (1998) 381-408
2. Beretta E., Solimano F., and Takeuchi Y. Global stability and periodic orbits for two patch predator-prey diffusion-delay models. Math. Biosci. 85 (1987) 153-183
3. Chen S., Wang F., and Young T. Positive periodic solution of two-species ratio-dependent predator-prey system with time delay in two-patch environment. Appl. Math. Comput. 150 (2004) 737-748
4. Chen S., Wang T., and Zhang J. Positive periodic solution for non-autonomous competition Lotka-Volterra patch system with time delay. Nonlinear Anal. RWA 5 (2004) 409-419
5. Ding X. Periodicity in a delayed semi-ratio-dependent predator-prey system. Appl. Math. J. Chinese Univ. Ser. B 20 (2005) 151-158
6. Gaines R.E., and Mawhin J.L. Coincidence Degree and Nonlinear Differential Equations (1977), Springer, Berlin
7. Gasull A., Kooij R.E., and Torrregrosa J. Limit cycles in Holling-Tanner model. Publ. Mat. 41 (1997) 149-167
8. Hsu S.-B., and Huang T.-W. Global stability for a class of predator-prey systems. SIAM J. Appl. Math. 55 (1995) 763-783
9. Ivlev V.S. Experimental Ecology of the Feeding of Fishes (1961), Yale University Press, New Haven, CT
10. Korobeinikov A. A Lyapunov function for Leslie-Gower predator-prey models. Appl. Math. Lett. 14 (2001) 697-699
11. Kuang Y., and Takeuchi Y. Predator-prey dynamics in models of prey dispersal in two-patch environments. Math. Biosci. 120 (1994) 77-98
12. Leslie P.H. Some further notes on the use of matrices in population mathematics. Biometrika 35 (1948) 213-245
13. Leslie P.H. A stochastic model for studying the properties of certain biological systems by numerical methods. Biometrika 45 (1958) 16-31
14. Levin S.A. Dispersion and population interactions. Am. Nat. 108 (1974) 207-228
15. May R.M. Stability and Complexity in Model Ecosystems (1974), Princeton University Press, Princeton, NJ
16. Ruan S., and Xiao D. Global analysis in a predator-prey system with nonmonotonic functional response. SIAM J. Appl. Math. 61 (2001) 1445-1472
17. Skellam J.D. Random dispersal in theoretical population. Miometrika 38 (1951) 196-216
18. Tanner J.T. The stability and the intrinsic growth rates of prey and predator populations. Ecology 56 (1975) 855-867
19. Xu R., Chaplain M.A.J., and Davidson F.A. Periodic solution for a delayed predator-prey model of prey dispersal in two-patch environments. Nonlinear Anal. RWA 5 (2004) 183-206
20. Xu R., and Chen L. Persistence and stability for two-species ratio-dependent predator-prey system with time delay in a two-patch environment. Comput. Math. Appl. 40 (2000) 577-588 2000
21. Wang Q., Fan M., and Wang K. Dynamics of a class of nonautonomous semi-ratio-dependent predator-prey systems with functional responses. J. Math. Anal. Appl. 278 (2003) 443-471
22. Wang W., and Ma Z. Asymptotic behavior of a predator-prey system with diffusion and delays. J. Math. Anal. Appl. 206 (1997) 191-204