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On finite-size Lyapunov exponents in multiscale systems
Lewis Mitchell1, Georg A Gottwald
1School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Lewis.Mitchell@uvm.edu
Chaos (Woodbury, N.Y.)
|July 5, 2012
Summary
Regime switches in multiscale systems create non-monotonic error growth rates. Finite size Lyapunov exponents (FSLEs) reveal signatures of slow and fast regimes, impacting predictability.
Area of Science:
- Dynamical Systems
- Chaos Theory
- Predictability Studies
Background:
- Multiscale systems exhibit complex dynamics with distinct slow and fast regimes.
- Error growth rates and predictability are crucial for understanding system behavior.
- Finite Size Lyapunov Exponents (FSLEs) are used to quantify error growth.
Purpose of the Study:
- To investigate the impact of regime switches on error growth rates and predictability in multiscale systems.
- To analyze how Finite Size Lyapunov Exponents (FSLEs) reflect the influence of different regimes.
Main Methods:
- Analysis of a dynamical system with slow and fast regimes and regime switches.
- Derivation of analytical results to explain observed phenomena.
- Numerical simulations to corroborate analytical findings.
- Examination of stochastic parametrizations for chaotic processes.
Main Results:
- Error growth rates can be non-monotonic with respect to initial error amplitude due to regime presence.
- Troughs in FSLE spectra indicate slow regimes; large peaks signify fast regimes where error growth exceeds maximal Lyapunov exponent estimates.
- Stochastic parametrizations of fast chaotic processes eliminate FSLE peaks, approximating large-scale predictability but not small-scale features.
Conclusions:
- Regime switches significantly alter error growth dynamics and predictability in multiscale systems.
- FSLE spectra provide distinct signatures for slow and fast regimes, offering insights into system predictability.
- Stochastic parametrizations can capture large-scale predictability but may fail to resolve fine-scale dynamics present in deterministic models.
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