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DY: Fachverband Dynamik und Statistische Physik

DY 63: Nonlinear Stochastic Systems

DY 63.1: Vortrag

Freitag, 13. März 2026, 11:30–11:45, ZEU/0118

Stochastic Dynamics of Noisy Oscillators under Eigenfunction Transformation — •Georg Podhaisky^1,2, Alberto Pérez-Cervera³, and Benjamin Lindner^1,2 — ¹Bernstein Center for Computational Neuroscience, Berlin, Germany — ²Humboldt University, Berlin, Germany — ³Universitat d’Alacant, Alicante, Spain

Stochastic oscillations are observed for a wide range of systems in biology and physics. Although their dynamics may vary drastically, a simple approach for a unified description exists. As recently demonstrated by Pérez-Cervera et al. (PNAS 120, 2023), the first non-trivial eigenfunction Q₁^*(x) of the Kolmogorov backward operator, which is obtained from the adjoint Fokker-Planck equation, can be used as a particularly useful transformation rule: This eigenfunction maps the trajectories of a given stochastic oscillator to a complex-valued domain. In this domain the autocorrelation statistics as well as the system’s linear response are characterized by simple and qualitatively universal functions, regardless of the original dynamics. Here we study the stochastic dynamics in the Q₁^*(x) domain, specifically, a number of two-dimensional systems including the Stuart-Landau oscillator and the harmonic oscillation with damping and thermal noise.

Keywords: stochastic oscillations; Koopman operator; Fokker-Planck equation; stochastic differential equation