Coexistence for species sharing a predator

Journal of Differential Equations

Volumn 196, Issue 1, 2004, Pages 209-225

  Schreiber, Sebastian J ^a  

^a Dept of Economics and Thomas Jefferson Program in Public Policy at the College of William and Mary   (United States)

Author keywords

Almost sure permanence; Apparent competition; Non equilibrium coexistence; Permanence

Indexed keywords

EID: 0346401428     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00169-4     Document Type: Article

References (24)

1. G.J. Butler, H.I. Freedman, P. Waltman, Uniformly persistent systems, Proc. Amer. Math. Soc. 96 (1986) 425-430.
2. G.J. Butler, P. Waltman, Persistence in dynamical systems, J. Differential Equations 63 (1986) 255-263.
3. R.C. Churchill, Isolated invariant sets in compact metric spaces, J. Differential Equations 12 (1972) 330-352.
4. C. Conley, R. Easton, Isolated invariant sets and isolating blocks, Trans. Amer. Math. Soc. 158 (1971) 35-61.
5. B.M. Garay, Uniform persistence and chain recurrence, J. Math. Anal. Appl. 139 (1989) 372-382.
6. M.E. Gilpin, F.J. Ayala, Global models of growth and competition, Proc. Natl. Acad. Sci. 70 (1973) 3590-3593.
7. M.W. Hirsch, Differential topology, in: Graduate Texts in Mathematics, Vol. 33, Springer, New York, 1976.
8. M.W. Hirsch, C.C. Pugh, M. Shub, Invariant manifolds, in: Lecture Notes in Mathematics, Vol. 583, Springer, Berlin, 1977.
9. J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, 1998.
10. H. Hoi, H. Winkler, Predation on nests: a case of apparent competition, Oecologia 98 (1994) 436-440.
11. C.S. Holling, The functional response of invertebrate predators to prey densities, Mem. Entomol. Soc. Canada 48 (1966) 3-86.
12. R.D. Holt, Predation, apparent competition and the structure of prey communities, Theoret. Population Biol. 12 (1977) 197-229.
13. R.D. Holt, Spatial heterogeneity, indirect interactions, and the coexistence of prey species, Amer. Nat. 124 (1987) 337-406.
14. R.D. Holt, J.H. Lawton, Apparent competition and enemy-free space in insect host-parasitoid communities, Amer. Nat. 142 (1993) 623-645.
15. V. Hutson, A theorem on average Liapunov functions, Monatsh. Math. 98 (1984) 267-275.
16. V. Hutson, The stability under perturbations of repulsive sets, J. Differential Equations 76 (1988) 77-90.
17. V.A.A. Jansen, K. Sigmund, Shaken not stirred: on permanence in ecological communities, Theoret. Population Biol. 54 (1998) 195-201.
18. R. Karban, D. Hougen-Eitzmann, G. English-Loeb, Predator-mediated apparent competition between two herbivores that feed on grapevines, Oecologia 97 (1994) 508-511.
19. R. McGehee, R.A. Armstrong, Some mathematical problems concerning the ecological principle of competitive exclusion, J. Differential Equations 23 (1977) 30-52.
20. J. Montgomery, Cohomology of isolated invariant sets under perturbation, J. Differential Equations 13 (1973) 257-299.
21. S.J. Schreiber, On growth rates of subadditive functions for semiflows, J. Differential Equations 148 (1998) 334-350.
22. r robust permanence, J. Differential Equations (2000) 400-426.
23. P. Schuster, K. Sigmund, R. Wolff, Dynamical systems under constant organization 3: cooperative and competitive behavior of hypercycles, J. Differential Equations 32 (1979) 357-368.
24. J. Vandermeer, Contributions to the global analysis of 3-D Lotka-Volterra equations: dynamic boundedness and indirect interactions in the case of one predator and two prey, J. Theoret. Biol. 148 (1991) 545-561.