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Perturbation of a globally stable steady state
Author(s):
H.
L.
Smith;
P.
Waltman
Journal:
Proc. Amer. Math. Soc.
127
(1999),
447-453.
MSC (1991):
Primary 34C35, 34E10, 58F30
MathSciNet review:
1487341
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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:
- 1.
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- 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
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- 5.
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- 7.
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- 8.
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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:
10.1090/S0002-9939-99-04768-1
PII:
S 0002-9939(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
Copyright of article:
Copyright
1999,
American Mathematical Society
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