Under a Lie-algebra non-degeneracy condition, the top Lyapunov exponent of the slow-fast system (2.3) converges to E[λ(A(Z))] as the time-scale separation vanishes, implying ergodicity phase transitions in truncated fluid models.
A noise-induced transition in the Lorenz system
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abstract
We consider a stochastic perturbation of the classical Lorenz system in the range of parameters for which the origin is the global attractor. We show that adding noise in the last component causes a transition from a unique to exactly two ergodic invariant measures. The bifurcation threshold depends on the strength of the noise: if the noise is weak, the only invariant measure is Gaussian, while strong enough noise causes the appearance of a second ergodic invariant measure.
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Asymptotics of Lyapunov Exponents and Phase Transitions for Fluids with Degenerate Forcing
Under a Lie-algebra non-degeneracy condition, the top Lyapunov exponent of the slow-fast system (2.3) converges to E[λ(A(Z))] as the time-scale separation vanishes, implying ergodicity phase transitions in truncated fluid models.