Berlin 2018 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 72: Poster: Stoch. and Nonl. Dy., Modeling, Compl. Sys.

DY 72.9: Poster

Donnerstag, 15. März 2018, 15:30–18:00, Poster A

Stochastic Differential Equations Driven by Deterministic Chaotic Maps: Analytic Solutions of the Perron-Frobenius Equation — •Griffin Williams and Christian Beck — School of Mathematical Sciences, Queen Mary University of London, Mile End Road, E1 4NS UK

We consider discrete-time dynamical systems systems with a linear relaxation dynamics that are driven by deterministic chaotic forces. By perturbative expansion in a small time scale parameter, we derive from the Perron-Frobenius equation the corrections to ordinary Fokker-Planck equations in leading order of the time scale separation parameter. We present analytic solutions to the equations for the example of driving forces generated by N-th order Chebychev maps. The leading order corrections are universal for N≥ 4 but different for N=2 and N=3. We also study diffusively coupled Chebychev maps as driving forces.