We study a system consisting of two coupled phase oscillators in the presence of noise. This system is
used as a model for the cardiorespiratory interaction in wakefulness and anaesthesia. We show that longrange
correlated noise produces transitions between epochs with different n:m synchronisation ratios, as
observed in the cardiovascular system. Also, we see that, the smaller the noise (specially the one acting
on the slower oscillator), the bigger the synchronisation time, exactly as happens in anaesthesia compared
with wakefulness. The dependence of the synchronisation time on the couplings, in the presence of noise,
is studied; such dependence is softened by low-frequency noise. We show that the coupling from the slow
oscillator to the fast one (respiration to heart) plays a more important role in synchronisation. Finally, we
see that the isolines with same synchronisation time seem to be a linear combination of the two couplings.
We address the problem of interactions between the phase of cardiac and respiration oscillatory components.
The coupling between these two quantities is experimentally investigated by the theory of stochastic Markovian
processes. The so-called Markov analysis allows us to derive nonlinear stochastic equations for the reconstruction
of the cardiorespiratory signals. The properties of these equations provide interesting new insights into the
strength and direction of coupling which enable us to divide the couplings to two parts: deterministic and
stochastic. It is shown that the synchronization behaviors of the reconstructed signals are statistically identical
with original one.
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