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Reduced-order Description of Transient Instabilities and Computation of Finite-Time Lyapunov Exponents. (arXiv:1704.06366v1 [math.DS])
来源于:arXiv
High-dimensional chaotic dynamical systems can exhibit strongly transient
features. These are often associated with instabilities that have 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 com 查看全文>>