期刊
CHAOS
卷 27, 期 6, 页码 -出版社
AMER INST PHYSICS
DOI: 10.1063/1.4984627
关键词
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资金
- ARO [6710-EG-YIP]
- AFOSR [FA9550-16-1-0231]
- ONR [N00014-15-1-2381]
- DARPA [HR0011-14-1-0060]
- Directorate For Engineering
- Div Of Electrical, Commun & Cyber Sys [1462254] Funding Source: National Science Foundation
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have a finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g., long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here, we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy-Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples. Published by AIP Publishing.
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