Synchronization Of Self-sustained Oscillator Research Articles

Reply to “Comment on ‘Synchronization in a ring of four mutually coupled van der Pol oscillators: Theory and experiment’ ”

The validity of desynchronization in Fig. 2 [B. Nana and P. Woafo, Phys. Rev. E 74, 046213 (2006)] is justified by the fact that the oscillators are nonidentical (instead of identical as quoted in Perlikowski et al.) and by the role of phase differences in synchronization of self-sustained oscillators.

Method of studying the synchronization of self-sustained oscillations using continuous wavelet analysis of univariant data

A new method for detecting the synchronization of a self-sustained oscillator under an external action with a linearly increasing frequency is proposed. It is based on the continuous wavelet transformation of univariant data (scalar time series). The efficiency of the method is demonstrated with a modified asymmetric van der Pol oscillator, Rossler oscillator, and experimental physiological data. In the last case, synchronization between rhythmic processes of different order in the cardiovascular and respiratory systems of the man is dem- onstrated using only the time series of the R - R intervals.

Detecting synchronization of self-sustained oscillators using wavelet analysis of univariate data for variable external drive frequency

A new method based on the continuous wavelet transform of univariate data is proposed for detecting the synchronization of a self-sustained oscillator under external drive action with linear frequency modulation. The efficacy of the proposed method is demonstrated in application to a model van der Pol oscillator and experimental physiological data.

Synchronization of self-sustained oscillators by common white noise

We study the stability of self-sustained oscillations under the influence of external noise. For small-noise amplitude a phase approximation for the Langevin dynamics is valid. A stationary distribution of the phase is used for an analytic calculation of the maximal Lyapunov exponent. We demonstrate that for small noise the exponent is negative, which corresponds to synchronization of oscillators.

Modulation analysis of forced non-linear oscillators for biological modelling

The synchronization of self-sustained oscillations by a forcing oscillation is of interest in a number of biological models. It has been considered for circadian rhythm modelling, heart-rate variability studies and forced breathing experiments. Outside the range of synchronization, conditions of almost-entrainment occur in which changes in amplitude and/or frequency are apparent. It is shown in this paper that such conditions can be analysed as modulation phenomena using the analytical method of harmonic balance. The degree of non-linearity in the self-sustained oscillation affects the nature of modulation, in that increasing distortion gives a trend towards frequency rather than amplitude modulation. The analytical results compare favourably with spectral analysis of simulated oscillators.