Lyapunov Exponents of Two Stochastic Lorenz 63 Systems
| Autor: | Bernardus J. Geurts, Erwin Luesink, Darryl D. Holm |
|---|---|
| Přispěvatelé: | Multiscale Modeling and Simulation |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Chaotic
UT-Hybrid-D FOS: Physical sciences Lyapunov exponent Dynamical Systems (math.DS) Expected value Dynamical system 01 natural sciences Noise (electronics) 010305 fluids & plasmas symbols.namesake 0103 physical sciences FOS: Mathematics Applied mathematics Volume contraction Mathematics - Dynamical Systems 010306 general physics Mathematical Physics Mathematics Advection Multiplicative function Fluid Dynamics (physics.flu-dyn) Statistical and Nonlinear Physics Physics - Fluid Dynamics Nonlinear Sciences::Chaotic Dynamics symbols |
| Zdroj: | Journal of statistical physics, 179(5-6), 1343-1365. Springer |
| ISSN: | 0022-4715 |
| Popis: | Two different types of perturbations of the Lorenz 63 dynamical system for Rayleigh-Benard convection by multiplicative noise -- called stochastic advection by Lie transport (SALT) noise and fluctuation-dissipation (FD) noise -- are found to produce qualitatively different effects, possibly because the total phase-space volume contraction rates are different. In the process of making this comparison between effects of SALT and FD noise on the Lorenz 63 system, a stochastic version of a robust deterministic numerical algorithm for obtaining the individual numerical Lyapunov exponents was developed. With this stochastic version of the algorithm, the value of the sum of the Lyapunov exponents for the FD noise was found to differ significantly from the value of the deterministic Lorenz 63 system, whereas the SALT noise preserves the Lorenz 63 value with high accuracy. The Lagrangian averaged version of the SALT equations (LA SALT) is found to yield a closed deterministic subsystem for the expected solutions which is found to be isomorphic to the original Lorenz 63 dynamical system. The solutions of the closed chaotic subsystem, in turn, drive a linear stochastic system for the fluctuations of the LA SALT solutions around their expected values. Comment: 19 pages, 4 figures, comments always welcome! |
| Databáze: | OpenAIRE |
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