Coherence Resonance Near a Hopf Bifurcation

Abstract

We report on the observation of coherence resonance for a semiconductor laser with short optical feedback close to Hopf bifurcations. Noise-induced self-pulsations are documented by distinct Lorentzian-like features in the power spectrum. The character of coherence is critically related to the type of the bifurcation. In the supercritical case, spectral width and height of the peak are monotonic functions of the noise level. In contrast, for the subcritical bifurcation, the width exhibits a minimum, translating into resonance behavior of the correlation time in the pulsation transients. A theoretical analysis based on the generic model of a self-sustained oscillator demonstrates that these observations are of general nature and are related to the fact that the damping depends qualitatively different on the noise intensity for the subcritical and supercritical case.

Spontaneous movements and linear response of a noisy oscillator

“…6 shows a similarly good agreement between the different numerical results (estimation by stochastic simulations and via the numerical solution for Q) and our approximation. Note that for the power spectrum other approximations have been derived (see [5,6] and references therein) whereas we are not aware of any other analytical approach for the calculation of the susceptibility.…”

“…This nonlinear transformation separates the generic dynamical part of the nonlinearities (surviving in the Hopf normal form) from system-specific nonlinearities (included in the nonlinear transformation). By adding noise to this normal form, one can describe the spontaneous activity of a noisy oscillator [2][3][4][5][6] as well as the response to a periodic driving. With a stochastic driving included in the dynamics, it is not possible to talk about bifurcation points anymore -the term bifurcation region coined by Meunier and Verga [7] is more appropriate.…”

A mean-field approach to elastically coupled hair bundles

“…The corresponding quality factor, when displayed as a function of system size, i.e. ε = 1/N 2 , goes through a shallow maximum, indicative of coherence resonance [36,8]. At about N 2 = 100 it drops below one, i.e.…”

Hysteresis of ionization waves

“…It is even possible to superimpose current noise at different amplitudes to perform a variety of studies relevant to topical aspects of non-linear physics, e.g. the behavior of saturated waves with superposed artificial noise [2] which is accessible in discharges [3]. Furthermore, there is a variety of investigations addressing different topics of non-linear behavior in these plasmas, e.g.…”