Free Access
Issue
ESAIM: M2AN
Volume 37, Number 2, March/April 2003
Page(s) 339 - 344
DOI https://doi.org/10.1051/m2an:2003029
Published online 15 November 2003
  1. V.D. Adams, D.L. DeAngelis and R.A. Goldstein, Stability analysis of the time delay in a Host-Parasitoid Model. J. Theoret. Biol. 83 (1980) 43-62. [CrossRef]
  2. E. Beretta and Y. Kuang, Convergence results in a well known delayed predator-prey system. J. Math. Anal. Appl. 204 (1996) 840-853. [CrossRef] [MathSciNet]
  3. A.A. Berryman, The origins and evolution of predator-prey theory. Ecology 73 (1992) 1530-1535. [CrossRef]
  4. Y. Cao and H.I. Freedman, Global attractivity in time delayed predator-prey system. J. Austral. Math. Soc. Ser. B. 38 (1996) 149-270. [CrossRef] [MathSciNet]
  5. B.W. Dale, L.G. Adams and R.T. Bowyer, Functional response of wolves preying on barren ground caribou in a multiple prey ecosystem. J. Anim. Ecology 63 (1994) 644-652. [CrossRef]
  6. M. Farkas and H.I. Freedman, The stable coexistence of competing species on a renewable resource. 138 (1989) 461-472.
  7. H.I. Freedman and V.S.H. Rao, The trade-off between mutual interface and time lags in predator-prey systems. Bull. Math. Biol. 45 (1983) 991-1004. [MathSciNet]
  8. J.K. Hale and P. Waltman, Persistence in infinite dimensional systems. SIAM J. Math. Anal. 20 (1989) 388-395. [CrossRef] [MathSciNet]
  9. Y. Kuang, Non uniqueness of limit cycles of Gause type predator-prey systems. Appl. Anal. 29 (1988) 269-287. [CrossRef] [MathSciNet]
  10. Y. Kuang, On the location and period of limit cycles in Gause type predator-prey systems. J. Math. Anal. Appl. 142 (1989) 130-143. [CrossRef] [MathSciNet]
  11. Y. Kuang, Limit cycles in a chemostat related model. SIAM J. Appl. Math. 49 (1989) 1759-1767. [CrossRef] [MathSciNet]
  12. Y. Kuang, Global stability of Gause type predator-prey systems. J. Math. Biol. 28 (1990) 463-474. [MathSciNet]
  13. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics. Academic Press, San Diego (1993).
  14. Y. Kuang and H.I. Freedman, Uniqueness of limit cycles in Gause type predator-prey systems. Math. Biosci. 88 (1988) 67-84. [CrossRef] [MathSciNet]
  15. R.M. May, Time-delay versus stability in population models with two and three trophic levels. Ecology 54 (1973) 315-325. [CrossRef]
  16. D. Mukherjee and A.B. Roy, Uniform persistence and global attractivity theorem for generalized prey-predator system with time delay. Nonlinear Anal. 38 (1999) 59-74. [CrossRef] [MathSciNet]
  17. R.E. Ricklefs and G.L. Miller, Ecology. W.H. Freeman and Company, New York (2000).
  18. C.E. Taylor and R.R. Sokal, Oscillations of housefly population sizes due to time lags. Ecology 57 (1976) 1060-1067. [CrossRef]
  19. B.G. Vielleux, An analysis of the predatory interactions between Paramecium and Didinium, J. Anim. Ecol. 48 (1979) 787-803. [CrossRef]
  20. W.D. Wang and Z.E. Ma, Harmless delays for uniform persistence. J. Math. Anal. Appl. 158 (1991) 256-268. [CrossRef] [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you