On Using Curvature to Demonstrate Stability

A new approach for demonstrating the global stability of ordinary differential equations is given. It is shown that if the curvature of solutions is bounded on some set, then any nonconstant orbits that remain in the set, must contain points that lie some minimum distance apart from each other. This...

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Bibliographic Details
Published in:Differential equations & nonlinear mechanics 2008, Vol.2008 (2008), p.1-7
Main Author: McCluskey, C. Connell
Format: Article
Language:English
Subjects:
Ordinary differential equations
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Summary:A new approach for demonstrating the global stability of ordinary differential equations is given. It is shown that if the curvature of solutions is bounded on some set, then any nonconstant orbits that remain in the set, must contain points that lie some minimum distance apart from each other. This is used to establish a negative-criterion for periodic orbits. This is extended to give a method of proving an equilibrium to be globally stable. The approach can also be used to rule out the sudden appearance of large-amplitude periodic orbits.
ISSN:1687-9643
1687-4099
1687-9651
1687-4102
DOI:10.1155/2008/745242