Index of content:
Volume 26, Issue 2, February 2016
- REGULAR ARTICLES
26(2016); http://dx.doi.org/10.1063/1.4940762View Description Hide Description
We propose a model for heart rate variability (HRV) of a healthy individual during sleep with the assumption that the heart rate variability is predominantly a random process. Autonomic nervous system activity has different properties during different sleep stages, and this affects many physiological systems including the cardiovascular system. Different properties of HRV can be observed during each particular sleep stage. We believe that taking into account the sleep architecture is crucial for modeling the human nighttime HRV. The stochastic model of HRV introduced by Kantelhardt et al. was used as the initial starting point. We studied the statistical properties of sleep in healthy adults, analyzing 30 polysomnographic recordings, which provided realistic information about sleep architecture. Next, we generated synthetic hypnograms and included them in the modeling of nighttime RR interval series. The results of standard HRV linear analysis and of nonlinear analysis (Shannon entropy, Poincaré plots, and multiscale multifractal analysis) show that—in comparison with real data—the HRV signals obtained from our model have very similar properties, in particular including the multifractal characteristics at different time scales. The model described in this paper is discussed in the context of normal sleep. However, its construction is such that it should allow to modelheart rate variability in sleep disorders. This possibility is briefly discussed.
The role of asymmetrical and repulsive coupling in the dynamics of two coupled van der Pol oscillators26(2016); http://dx.doi.org/10.1063/1.4940967View Description Hide Description
A system of two asymmetrically coupled van der Pol oscillators has been studied. We show that the introduction of a small asymmetry in coupling leads to the appearance of a “wideband synchronization channel” in the bifurcational structure of the parameter space. An increase of asymmetry and transition to repulsive interaction leads to the formation of multistability. As the result, the tip of the Arnold's tongue widens due to the formation of folds defined by saddle-node bifurcation curves for the limit cycles on the torus.
26(2016); http://dx.doi.org/10.1063/1.4940236View Description Hide Description
Gambles are random variables that model possible changes in wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but their generality limits predictive power. Expectation value maximizers are defined as rational in economics, but expectation values are only meaningful in the presence of ensembles or in systems with ergodic properties, whereas decision-makers have no access to ensembles, and the variables representing wealth in the usual growth models do not have the relevant ergodic properties. Simultaneously addressing the shortcomings of utility and those of expectations, we propose to evaluate gambles by averaging wealth growth over time. No utility function is needed, but a dynamic must be specified to compute time averages. Linear and logarithmic “utility functions” appear as transformations that generate ergodic observables for purely additive and purely multiplicative dynamics, respectively. We highlight inconsistencies throughout the development of decision theory, whose correction clarifies that our perspective is legitimate. These invalidate a commonly cited argument for bounded utility functions.
26(2016); http://dx.doi.org/10.1063/1.4941376View Description Hide Description
A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.