Dresden 2014 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 10: Nonlinear Stochastic Systems
DY 10.9: Talk
Tuesday, April 1, 2014, 11:45–12:00, ZEU 160
Spectra of delay-coupled heterogeneous noisy nonlinear oscillators — •Andrea Vüllings1, Eckehard Schöll1, and Benjamin Lindner2,3 — 1Institut für Theoretische Physik, TU Berlin — 2Physics Department, Humboldt University Berlin — 3Bernstein Center for Computational Neuroscience Berlin
We study the spectral statistics (power and cross-spectral densities) of a small number of noisy nonlinear oscillators and derive analytical approximations for these spectra. The individual oscillators are described by the normal form of a supercritical or subcritical Hopf bifurcation supplemented by Gaussian white noise. Oscillators can be distinguished from each other by their frequency, bifurcation parameter, and noise intensity. Extending previous results from the literature, we first calculate in linear response theory the power spectral density and response function of the single oscillator in both super- and subcritical parameter. For small heterogeneous groups of oscillators (N = 2 or 3), which are coupled by a delayed linear term, we use a linear response ansatz to derive approximations for the power and cross-spectral densities of the oscillators within this small network. Using the theory we relate the peaks in the spectra of the homogeneous system (identical oscillators) to periodic solutions of the deterministic (noiseless) system. For two delay-coupled subcritical Hopf oscillators, we show that the coupling can enhance the coherence resonance effect, which is known to occur for the single subcritical oscillator. In the case of heterogeneous oscillators, we find that the delay-induced characteristic profile of the spectra is conserved for moderate frequency detuning.