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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Main Author:	C. Connell McCluskey
Format:	Article
Language:	English
Published:	Hindawi Limited 2008-01-01
Series:	Differential Equations and Nonlinear Mechanics
Online Access:	http://dx.doi.org/10.1155/2008/745242

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spelling	doaj-6a4e3fa83f2744de97aa38e8cf3fe9b42020-11-24T21:25:10ZengHindawi LimitedDifferential Equations and Nonlinear Mechanics1687-40991687-41022008-01-01200810.1155/2008/745242745242On Using Curvature to Demonstrate StabilityC. Connell McCluskey0Department of Mathematics, Wilfrid Laurier University, 75 University Ave West, Waterloo, ON, N2L 3C5, CanadaA 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.http://dx.doi.org/10.1155/2008/745242
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	C. Connell McCluskey
spellingShingle	C. Connell McCluskey On Using Curvature to Demonstrate Stability Differential Equations and Nonlinear Mechanics
author_facet	C. Connell McCluskey
author_sort	C. Connell McCluskey
title	On Using Curvature to Demonstrate Stability
title_short	On Using Curvature to Demonstrate Stability
title_full	On Using Curvature to Demonstrate Stability
title_fullStr	On Using Curvature to Demonstrate Stability
title_full_unstemmed	On Using Curvature to Demonstrate Stability
title_sort	on using curvature to demonstrate stability
publisher	Hindawi Limited
series	Differential Equations and Nonlinear Mechanics
issn	1687-4099 1687-4102
publishDate	2008-01-01
description	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.
url	http://dx.doi.org/10.1155/2008/745242
work_keys_str_mv	AT cconnellmccluskey onusingcurvaturetodemonstratestability
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On Using Curvature to Demonstrate Stability

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