Lyapunov Exponents of Two Stochastic Lorenz 63 Systems

Abstract

Two different types of perturbations of the Lorenz 63 dynamical system for Rayleigh-Bénard convection by multiplicative noise -called stochastic advection by Lie transport (SALT) noise and fluctuationdissipation (FD) noise -are found to produce qualitatively different effects. For example, SALT noise preserves the sum of the deterministic Lyapunov exponents at any time, while FD noise does not. 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 differs from the deterministic value for the FD noise, whereas SALT noise retains this value with high accuracy.arXiv:1706.05882v6 [math.DS]

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