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On Using Curvature to Demonstrate Stability

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Author(s): C. Connell McCluskey

Journal: Differential Equations and Nonlinear Mechanics
ISSN 1687-4099

Volume: 2008;
Date: 2008;
Original page

ABSTRACT
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.
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