BACKGROUND/AIM Pneumocardiography (PNCG) is the recording method of cardiac-induced tracheal air flow and pressure pulsations in the respiratory airways. PNCG signals reflect both the lung and heart actions and could be accurately recorded in spontaneously breathing anesthetized rats. Nonlinear analysis methods, including the Lyapunov exponent, can be used to explain the biological dynamics of ...

In this paper, chaotic dynamic and nonlinear control in a glucose-insulin system in types I diabetic patients and a healthy person have been investigated. Chaotic analysis methods of the blood glucose system include Lyapunov exponent and power spectral density based on the time series derived from the clinical data. Wolf's algorithm is used to calculate the Lyapunov exponent, which positive val...

Distinct sleep phases are related to different dynamical patterns in electroencephalogram (EEG) signals. In this article, the relationship between the sleep stages and nonlinear behavior of sleep EEG is explored. In particular, analysis of approximate entropy (ApEn) and the largest Lyapunov exponent is evaluated in patients with sleep apnea, which is defined as respiratory flow that is suspende...

A non-vanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system, however no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ε = E/N , the energy per degree of freedom. The fu...

Three chaotic indicators, namely the correlation dimension, the Lyapunov exponent, and the Kolmogorov entropy, are estimated for one-year long hourly average NO (nitrogen monoxide), CO (carbon monoxide), SO2 (sulfur dioxide), PM10 (particles with an aerodynamic diameter of approximately 10 m or less), and NO2 (nitrogen dioxide) concentration to examine the possible chaotic characteristics in th...

We study Ruelle’s transfer operator L induced by a Cr+1–smooth expanding map φ of a smooth manifold and a Cr–smooth bundle automorphism Φ of a real vector bundle E . We prove the following exact formula for the essential spectral radius of L on the space Cr,α of r-times continuously differentiable sections of E with α-Hölder r-th derivative: ress(L;C) = exp ( sup ν∈Erg {hν + λν − (r + α)χν} ) ,...

When a dynamical system exhibits transient chaos and a nonchaotic attractor, as in a periodic window, noise can induce a chaotic attractor. In particular, when the noise amplitude exceeds a critical value, the largest Lyapunov exponent of the attractor of the system starts to increase from zero. While a scaling law for the variation of the Lyapunov exponent with noise was uncovered previously, ...

In this paper we have proposed a novel amplitude suppression algorithm for EEG signals collected during epileptic seizure. Then we have proposed a measure of chaoticity for a chaotic signal, which is somewhat similar to measuring sensitive dependence on initial conditions by measuring Lyapunov exponent in a chaotic dynamical system. We have shown that with respect to this measure the amplitude ...

Many digital signal processing, techniques have been used to automatically distinguish protein coding regions (exons) from non-coding regions (introns) in DNA sequences. In this work, we have characterized these sequences according to their nonlinear dynamical features such as moment invariants, correlation dimension, and largest Lyapunov exponent estimates. We have applied our model to a numbe...

We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits, depending on parameter values: (i) a continuous transition in the bounded Kardar-Parisi-Zhang universality class, with a zero largest Lyapunov exponent at the critic...