  In type I intermittency, simple models known for at least twenty years show
that a characteristic u-shaped probability distribution is obtained for the
laminar phase length. We have shown elsewhere that, for some cases of
pathology, the laminar phase length distribution characteristic for type I
intermittency may be obtained in human heart rate variability data. The heart
and its regulatory systems are presumed to be both noisy and nonstationary.
Although the effect of additive noise on the laminar phase distribution in type
I intermittency is well known, neither the effect of multiplicative noise nor
of nonstationarity (i.e. changes of the control parameter with the time) have
been studied. In this paper, we first discuss the properties of two classes of
models of type I intermittency: a) the control parameter of the logistic map is
changed dichotomously from a value within the intermittency range to just below
the bifurcation point and back; b) the control parameter is changed randomly
within the same parameter range as in the model class a). We show that the
properties of both models are importantly different from those obtained for
type I intermittency in the presence additive noise as obtained by Hirsch
twenty years ago. The two models help explain some of the features seen in the
intermittency in human heart rate variability.
