Successional stability of vector fields

in dimension three

Author:
Sebastian J. Schreiber

Journal:
Proc. Amer. Math. Soc. **127** (1999), 993-1002

MSC (1991):
Primary 34D30, 58F12; Secondary 92D40, 92D25

DOI:
https://doi.org/10.1090/S0002-9939-99-05169-2

MathSciNet review:
1641101

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Abstract | References | Similar Articles | Additional Information

Abstract: A topological invariant, the community transition graph, is introduced for dissipative vector fields that preserve the skeleton of the positive orthant. A vector field is defined to be successionally stable if it lies in an open set of vector fields with the same community transition graph. In dimension three, it is shown that vector fields for which the origin is a connected component of the chain recurrent set can be approximated in the Whitney topology by a successionally stable vector field.

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Additional Information

**Sebastian J. Schreiber**

Affiliation:
Department of Mathematics, Western Washington University, Bellingham, Washington 98225

Email:
sschreib@cc.wwu.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05169-2

Keywords:
Generic properties of vector fields,
ecological succession,
population dynamics

Received by editor(s):
January 28, 1997

Additional Notes:
Part of this research was completed during a postdoctoral fellowship sponsored by Andrew P. Gutierrez at the University of California, Berkeley. For his support and encouragement, the author is grateful.

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1999
American Mathematical Society