A Noise-Induced Transition in the Lorenz System
Michele Coti Zelati, Martin Hairer
Abstract
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.
Topics & Concepts
Ergodic theoryInvariant measureMathematicsInvariant (physics)Lorenz systemBifurcationPerturbation (astronomy)Statistical physicsMathematical analysisComplex systemBifurcation theoryErgodicityScale invarianceMeasure (data warehouse)Noise (video)White noiseNonlinear systemStochastic processBifurcation diagramPhysicsDynamical systems theorystochastic dynamics and bifurcationChaos control and synchronizationMathematical Dynamics and Fractals