Localized Instability and Attraction along Invariant Manifolds
Name
Haller-2010-Localized Instabilit.pdf
Size
2.12 MB
Format
Adobe PDF
Checksum (MD5)
0d30b9d5b175b71e9bd35912321c78b3
Author(s)
Haller, George
Sapsis, Themistoklis
Date Issued
June 2010
Journal
SIAM Journal on Applied Dynamical Systems
Publisher
Society of Industrial and Applied Mathematics (SIAM)
Citation
Haller, George, and Themistoklis Sapsis. “Localized Instability and Attraction along Invariant Manifolds.” SIAM Journal on Applied Dynamical Systems 9 (2010): 611-633. ©2010 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We derive a simple criterion for transverse instabilities along a general invariant manifold of a multidimensional dynamical system. The criterion requires an appropriately defined normal infinitesimal Lyapunov exponent (NILE) to be positive over regions of transverse instability on the manifold. Unlike classic Lyapunov-type numbers in the theory of normally hyperbolic invariant manifolds, the NILE can be computed analytically in applications. This enables us to locate, for example, regions of transient jumping along an invariant manifold that is otherwise globally attracting. To illustrate our results, we determine the locations of intermittent instabilities in bubble motion past a cylinder, in predator-prey interactions, and in soft-stiff structural systems.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/08074324x
