OBJECTIVES Soft-computing techniques are commonly used to detect medical phenomena and to help with clinical diagnoses and treatment. The purpose of this paper is to analyze the single electroencephalography (EEG) signal with the chaotic methods in order to identify the sleep stages. METHODS Data acquisition (polysomnography) was performed on four healthy young adults (all males with a mean a...

We study the dynamics of systems with different time scales, when access only to the slow variables is allowed. We use the concept of Finite Size Lyapunov Exponent (FSLE) and consider both the case when the equations of motion for the slow components are known, and the situation when a scalar time series of one of the slow variables has been measured. A discussion on the effects of parameterizi...

Ideal power converters are governed by differential equations with discontinuous right-hand sides. General-purpose algorithms to compute their Lyapunov exponents assume smooth equations, so are not directly applicable to power electronics. We review the methods and their problems, focusing on the largest Lyapunov exponent, which dominates system behavior. The variational approach can incorporat...

Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems in the neighborhood of a saddle node bifurcation whereby a strange attractor is replaced by a periodic (torus) attractor. This transition is accompanied by Type-I intermittency. The largest nontrivial Lyapunov exponent Λ is a good order–parameter for this route from chaos to SNA to periodic motion: the signature is di...

The convergence of the Lyapunov vector toward its asymptotic shape is investigated in two different one-dimensional Hamiltonian lattices: the so-called Fermi-Pasta-Ulam and Phi(4) chains. In both cases, we find an anomalous behavior, i.e., a clear difference from the previously conjectured analogy with the Kardar-Parisi-Zhang equation. The origin of the discrepancy is eventually traced back to ...

Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov exponent, as well as through the characteristic distributions of finite time Lyapunov exponents. Strange nonchaotic attractors can be created at a saddle–node bif...

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, λ and λ respectively. We discuss the numerical difficulties that arise in the numerical calculation of λ in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically λ by using a cumulant ...