Positive periodic solutions in delayed Gause-type predator-prey systems

Journal of Mathematical Analysis and Applications

Volumn 339, Issue 2, 2008, Pages 1220-1230

  Ding, Xiaoquan ^a,b   Jiang, Jifa ^a  

^a TONGJI UNIVERSITY   (China)

^b SHANDONG AGRICULTURAL UNIVERSITY   (China)

Author keywords

Coincidence degree; Periodic solution; Predator prey system; Time delay

Indexed keywords

EID: 35349024817     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.07.079     Document Type: Article

References (19)

1. Aghajani A., and Moradifam A. Nonexistence of limit cycles in two classes of predator-prey systems. Appl. Math. Comput. 175 (2006) 356-365
2. Allee W.C. Animal aggregation. Quart. Rev. Biol. 2 (1927) 367-398
3. Fan M., and Wang K. Global existence of positive periodic solution of a predator-prey system with Holling type II functional response. Acta Math. Sci. Ser. A Chin. Ed. 21 4 (2001) 492-497 (in Chinese)
4. Freedman H.I., and Wu J. Periodic solutions of single species models with periodic delay. SIAM J. Math. Anal. Appl. 23 (1992) 689-701
5. Gaines R.E., and Mawhin J.L. Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag, Berlin
6. Gilpin M.E., and Ayala F.G. Global models of growth and competition. Proc. Natl. Acad. Sci. USA 70 (1973) 3590-3593
7. 2 (t - τ)]. Qurt. Appl. Math. 3 (1990) 433-440
8. Hasik K. Uniqueness of limit cycles in predator-prey system: The role of weight functions. J. Math. Anal. Appl. 277 (2003) 130-141
9. Hsu S.B., and Huang T.W. Global stability for a class of predator-prey systems. SIAM. J. Math. Appl. 55 (1995) 763-783
10. Hu X., Liu G., and Yan J. Existence of multiple positive periodic solutions of delayed predator-prey models with functional responses. Comput. Math. Appl. 52 (2006) 1453-1462
11. Hwang T.W. Uniqueness of the limit cycle for predator-prey systems. J. Math. Anal. Appl. 238 (1999) 179-195
12. Kooij R.E., and Zegeling A. Qualitative properties of two-dimensional predator-prey systems. Nonlinear Anal. 6 (1997) 693-715
13. Kuang Y. Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press, New York
14. Kuang Y. Global stability of Gause-type predator-prey systems. J. Math. Biol. 28 (1990) 463-474
15. Li Y., and Kuang Y. Periodic solutions of periodic delay Lotka-Volterra equations and systems. J. Math. Anal. Appl. 255 (2001) 260-280
16. Smith F.E. Population dynamics in Daphnia Magna and a new model for population growth. Ecology 44 (1963) 651-663
17. Sugie J. Two parameters bifurcation in a predator-prey system of Ivlev type. J. Math. Anal. Appl. 222 (1998) 349-371
18. Ye D., Fan M., and Zhang W. Existence of nontrivial positive periodic solution of a predator-prey system with Holling type II functional response. Chinese J. Eng. Math. 21 4 (2004) 504-508 (in Chinese)
19. Zhao C.J. On a periodic predator-prey system with time delays. J. Math. Anal. Appl. 331 (2007) 978-985