Document Type
Article
Publication Date
2008
Department
Mathematics
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.
Recommended Citation
McCluskey, C. Connell, "On Using Curvature to Demonstrate Stability" (2008). Mathematics Faculty Publications. 31.
https://scholars.wlu.ca/math_faculty/31
Comments
This article was originally published in Differential Equations and Nonlinear Mechanisms, 2008: Article ID 745242. © 2008 The Author.