Localized Instability and Attraction along Invariant Manifolds
Author(s)
Haller, George; Sapsis, Themistoklis
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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.
Date issued
2010-06Department
Massachusetts Institute of Technology. Department of Mechanical EngineeringJournal
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
ISSN
1536-0040