Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Perturbation of a globally stable steady state


Authors: H. L. Smith and P. Waltman
Journal: Proc. Amer. Math. Soc. 127 (1999), 447-453
MSC (1991): Primary 34C35, 34E10, 58F30
DOI: https://doi.org/10.1090/S0002-9939-99-04768-1
MathSciNet review: 1487341
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that within a parameterized family of semi-dynamical systems enjoying a mild uniform dissipative condition, the property that a locally asymptotically stable steady state is globally attracting is an open condition in the parameters.


References [Enhancements On Off] (What's this?)

  • 1. Amann, H. (1976) Fixed Point equations and nonlinear eigenvalue problems in ordered Banach Spaces, SIAM Rev. 18, 620-709. MR 54:3519; MR 57:7269
  • 2. Butler, G. and Waltman, P. (1986) Persistence in dynamical systems, J. Diff. Eqns. 63, 255-263. MR 87k:54058
  • 3. Butler, G., Freedman, H. and Waltman, P. (1986) Uniformly persistent systems, Proc. Amer. Math. Soc. 96, 425-430. MR 87d:58119
  • 4. Hale, J. and Waltman, P. (1989) Persistence in infinite dimensional systems, SIAM J. Math. Anal. 20, 388-395. MR 90b:58156
  • 5. Krasnosels'kii, M.A. (1964) Positive solutions of Operator Equations, P. Noordhoff, Groningen, the Netherlands. MR 31:6107
  • 6. Smith, H.L. (1982) On the basin of attraction of a perturbed attractor, Nonlinear Analysis, 6, 911-917. MR 84i:58077
  • 7. Smith, H.L. (1995), Monotone Dynamical Systems: An introduction to the Theory of Competitive and Cooperative Systems AMS Math. Surv.& Monographs, 41, Providence, R.I. MR 96c:34002
  • 8. Smith, H. and Waltman, P. (1995) The Theory of the Chemostat, Cambridge Univ. Press. MR 96e:92016
  • 9. Thieme, H. R. (1993) Persistence under relaxed point-dissipativity (with application to an epidemic model), SIAM J. Math. Anal. 24, 407-435. MR 94a:34055
  • 10. Zeidler, E. (1986) Nonlinear Functional Analysis and its Applications, Springer-Verlag, New York. MR 87f:47083

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34C35, 34E10, 58F30

Retrieve articles in all journals with MSC (1991): 34C35, 34E10, 58F30


Additional Information

H. L. Smith
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287–1804
Email: halsmith@asu.edu

P. Waltman
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Email: waltman@mathcs.emory.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04768-1
Received by editor(s): May 20, 1997
Additional Notes: The first author was supported by NSF Grant DMS 9300974, and the second author was supported by NSF Grant DMS 9424592 and an award from the University Research Council of Emory University
Communicated by: Linda Keen
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society