Search results for "Chaotic"

Nonlinear analysis of sleep EEG data in schizophrenia: calculation of the principal Lyapunov exponent

1995

The generating mechanism of the electroencephalogram (EEG) points to the hypothesis that EEG signals derive from a nonlinear dynamic system. Hence, the unpredictability of the EEG might be considered as a phenomenon exhibiting its chaotic character. The essential property of chaotic dynamics is the so-called sensitive dependence on initial conditions. This property can be quantified by calculating the system's first positive Lyapunov exponent, L1. We calculated L1 for sleep EEG segments of 13 schizophrenic patients and 13 control subjects that corresponded to sleep stages I, II, III, IV and REM (rapid eye movement), as defined by Rechtschaffen and Kales, for the lead positions Cz and Pz. Du…

Nonlinear analysis of sleep eeg in depression: Calculation of the largest lyapunov exponent

1995

Conventional sleep analysis according to Rechtschaffen and Kales (1968) has provided meaningful contributions to the understanding of disturbed sleep architecture in depression. However, there is no characteristic alteration of the sleep cycle, which could serve as a highly specific feature for depressive illness. Therefore, we started to investigate nonlinear properties of sleep electroencephalographic (EEG) data in order to elucidate functional alterations other than those obtained from classical sleep analysis. The application of methods from nonlinear dynamical system theory to EEG data has led to the assumption that the EEG can be treated as a deterministic chaotic process. Chaotic sys…

Dynamics of differentiation and integration operators on weighted spaces of entire functions

2014

Almost Planar Homoclinic Loops in R3

1996

AbstractIn this paper we study homoclinic loops of vector fields in 3-dimensional space when the two principal eigenvalues are real of opposite sign, which we call almost planar. We are interested to have a theory for higher codimension bifurcations. Almost planar homoclinic loop bifurcations generically occur in two versions “non-twisted” and “twisted” loops. We consider high codimension homoclinic loop bifurcations under generic conditions. The generic condition forces the existence of a 2-dimensional topological invariant ring (non necessarily unique), which is a topological cylinder in the “non-twisted” case and a topological Möbius band in the “twisted” case. If the third eigenvalue is…

Porosities and dimensions of measures

1999

We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.

On the number of solutions of a Duffing equation

1991

The exact number of solutions of a Duffing equation with small forcing term and homogeneous Neumann boundary conditions is given. Several bifurcation diagrams are shown.

A Hardware and Secure Pseudorandom Generator for Constrained Devices

2018

Hardware security for an Internet of Things or cyber physical system drives the need for ubiquitous cryptography to different sensing infrastructures in these fields. In particular, generating strong cryptographic keys on such resource-constrained device depends on a lightweight and cryptographically secure random number generator. In this research work, we have introduced a new hardware chaos-based pseudorandom number generator, which is mainly based on the deletion of an Hamilton cycle within the $N$ -cube (or on the vectorial negation), plus one single permutation. We have rigorously proven the chaotic behavior and cryptographically secure property of the whole proposal: the mid-term eff…

A new method for optimal synthesis of wavelet-based neural networks suitable for identification purposes

1999

Abstract This paper deals with a new method for optimal synthesis of Wavelet-Based Neural Networks (WBNN) suitable for identification purposes. The method uses a genetic algorithm (GA) combined with a steepest descent technique and least square techniques for both optimal selection of the structure of the WBNN and its training. The method is applied for designing a predictor for a chaotic temporal series

Estimation of Granger causality through Artificial Neural Networks: applications to physiological systems and chaotic electronic oscillators

2021

One of the most challenging problems in the study of complex dynamical systems is to find the statistical interdependencies among the system components. Granger causality (GC) represents one of the most employed approaches, based on modeling the system dynamics with a linear vector autoregressive (VAR) model and on evaluating the information flow between two processes in terms of prediction error variances. In its most advanced setting, GC analysis is performed through a state-space (SS) representation of the VAR model that allows to compute both conditional and unconditional forms of GC by solving only one regression problem. While this problem is typically solved through Ordinary Least Sq…

Role of the reagents consumption in the chaotic dynamics of the Belousov-Zhabotitinsky oscillator in closed unstirred reactors

2010

Chemical oscillations generated by the Belousov–Zhabotinsky reaction in batch unstirred reactors, show a characteristic chaotic transient in their dynamical regime, which is generally found between two periodic regions. Chemical chaos starts and finishes by following a direct and an inverse Ruelle–Takens–Newhouse scenario, respectively. In previous works we showed, both experimentally and theoretically, that the complex oscillations are generated by the coupling among the nonlinear kinetics and the transport phenomena, the latter due to concentration and density gradients. In particular, convection was found to play a fundamental role. In this paper, we develop a reaction–diffusion–convecti…