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2008 On Using Curvature to Demonstrate Stability
C. Connell McCluskey
Differ. Equ. Nonlinear Mech. 2008: 1-7 (2008). DOI: 10.1155/2008/745242


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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C. Connell McCluskey. "On Using Curvature to Demonstrate Stability." Differ. Equ. Nonlinear Mech. 2008 1 - 7, 2008.


Received: 11 September 2007; Revised: 28 February 2008; Accepted: 2 April 2008; Published: 2008
First available in Project Euclid: 26 January 2017

zbMATH: 1158.34034
MathSciNet: MR2399646
Digital Object Identifier: 10.1155/2008/745242

Rights: Copyright © 2008 Hindawi


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