Rocky Mountain Journal of Mathematics

Invasion of a persistent system

Gail S.K. Wolkowicz

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 20, Number 4 (1990), 1217-1234.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181073071

Digital Object Identifier
doi:10.1216/rmjm/1181073071

Mathematical Reviews number (MathSciNet)
MR1096580

Zentralblatt MATH identifier
0724.92025

Citation

Wolkowicz, Gail S.K. Invasion of a persistent system. Rocky Mountain J. Math. 20 (1990), no. 4, 1217--1234. doi:10.1216/rmjm/1181073071. https://projecteuclid.org/euclid.rmjm/1181073071


Export citation

References

  • N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, Grundlehren math. Wissensch. 161, Springer-Verlag, 1970.
  • G. J. Butler, H. I. Freedman and P. Waltman, Persistence in dynamical systems models of three-population ecological communities in Differential Equations: Qualitative Theory, Colloquia Mathematica Societatis János Bolya\`\i, Szeged, Hungary 47 (1984), 167-178.
  • --------, Uniformly persistent systems, Proc. Amer. Math. Soc. 96 (1986), 425-430.
  • G. J. Butler and P. Waltman, Persistence in dynamical systems, J. Differential Equations 63 (1986), 255-263.
  • G. J. Butler and G. S. K. Wolkowicz, A mathematical model of the chemostat with a general class of functions describing nutrient uptake, SIAM J. Appl. Math. 45 (1985), 138-151.
  • --------, Predator-mediated competition in a chemostat, J. Math. Biol. 24 (1986), 167-191.
  • C. Conley, Isolated invariant sets and the morse index, Regional Conference Series in Mathematics 38 Amer. Math. Soc., 1978.
  • T. C. Gard, Uniform persistence in multispecies population models, Math. Biosci. 85 (1987), 93-104.
  • J. Hofbauer, General cooperation theorem for hypercycles, Monatsh. Math. 91 (1981), 233-240.
  • --------, A unified approach to persistence, Selected Topics in Biomathematics, Proceedings of a Conference in Laxenburg, 1987.
  • J. Hofbauer and K. Sigmund, Dynamical systems and the theory of evolution, Cambridge University Press, 1988.
  • S. B. Hsu, S. Hubbell and P. Waltman, A mathematical theory of single-nutrient competition in continuous cultures for microorganisms, SIAM J. Appl. Math. 32 (1977), 366-383.
  • V. Hutson, A theorem on average Liapunov functions, Monatsh. Math. 98 (1984), 267-275.
  • -------- and R. Law, Permanent coexistence in general models of three interacting species, J. Math. Biol. 21 (1985), 289-298.
  • G. R. Sell, Topological dynamics and ordinary differential equations, Van Nostrand Reinhold Mathematical Studies 33, 1971.
  • K. Sigmund and P. Schuster, Permanence and uninvadability for deterministic population models, in : Stochastic Phenomena and Chaotic Behaviour in Complex Systems, Synergetics LNM, vol. 31, Springer, Berlin, 1984.
  • G. S. K. Wolkowicz, Successful invasion of a food web in a chemostat, Math. Biosci. 93 (1989), 249-268. \noindent D\sixpoint EPARTMENT OF \eightpoint M\sixpoint ATHEMATICS AND M\sixpoint ASTER \eightpoint U\sixpoint NIVERSITY,\eightpoint H\sixpoint AMILTON, \eightpoint O\sixpoint NTARIO, \eightpoint C\sixpoint ANADA