Type I intermittency in nonstationary systems—models and human heart rate variability

Abstract

Type I intermittency occurs whenever a discrete dynamical system in a chaotic state is about to undergo a tangential bifurcation. Then long stretches of (almost) periodic behavior (laminar phases) occur. These laminar phases are interspersed with chaotic behavior. In type I intermittency, simple models show that a characteristic U-shaped probability distribution is obtained for the laminar phase length. We have shown elsewhere that, in 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 usually presumed to be noisy. Although the effect of additive noise on the laminar phase distribution in type I intermittency is well known, the effect of multiplicative noise has not been studied. In this presentation, we discuss the properties of classes of models of type I intermittency in which the control parameter is changed randomly within the specified parameter range. We show that the properties of these models are importantly different from those obtained for type I intermittency in the presence of additive noise. We also show how the two models help explain some of the features seen in the intermittency in human heart rate variability. Some technical problems with measuring laminar phase lengths in time series will also be discussed.