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DY: Fachverband Dynamik und Statistische Physik
DY 18: Pattern Formation, Delay and Nonlinear Stochastic Systems
DY 18.4: Vortrag
Dienstag, 19. März 2024, 10:30–10:45, BH-N 128
A universal description of stochastic oscillators — Alberto Pérez-Cervera1, Boris Gutkin2, Peter J. Thomas3, and •Benjamin Lindner4,5 — 1Universidad Complutense de Madrid,Spain — 2Ecole Normale Supérieure - Paris Science Letters University, France — 3Case Western Reserve University, Cleveland, OH, USA — 4Institut für Physik, Humboldt-Universität zu Berlin — 5Bernstein Center for Computational Neuroscience Berlin
Systems in physics and biology exhibit oscillations which are shaped by randomness. Dynamically, such stochastic oscillations can be caused by different mechanisms and are thus described by strongly different mathematical models, e.g. a linear dynamics with a stable focus and noise, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to spikes. Here, we introduce a nonlinear transformation of stochastic oscillators to a complex-valued function that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different, weakly coupled oscillators. The general framework (see Perez-Cervera et al. PNAS 2023) can be applied to the different example dynamics mentioned above but also to higher-dimensional systems such as two damped harmonic oscillators with thermal noise that are strongly coupled.
Keywords: Noise and fluctuations; Oscillations and oscillators; Fluctuation-dissipation relations; Universal description