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Successional stability of vector fields in dimension three |
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| Authors: | Sebastian J. Schreiber |
| Affiliation: | Department of Mathematics, Western Washington University, Bellingham, Washington 98225 |
| 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. |
| Keywords: | Generic properties of vector fields ecological succession population dynamics |
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