Polarity balance for attractor self-reproducing.

There are complex chaotic manifolds in practical nonlinear dynamical systems, especially in nonlinear circuits and chemical engineering. Any system attractor has its own geometric and physical properties, such as granularity, orientation, and spatiotemporal distribution. Polarity balance plays an important role in the solution of a dynamical system including symmetrization, attractor merging, and attractor self-reproducing.

Predicting tipping points of dynamical systems during a period-doubling route to chaos.

Classical indicators of tipping points have limitations when they are applied to an ecological and a biological model. For example, they cannot correctly predict tipping points during a period-doubling route to chaos. To counter this limitation, we here try to modify four well-known indicators of tipping points, namely the autocorrelation function, the variance, the kurtosis, and the skewness.

Applied Chaos Level Test for Validation of Signal Conditions Underlying Optimal Performance of Voice Classification Methods.

Purpose: The purpose of this study is to introduce a chaos level test to evaluate linear and nonlinear voice type classification method performances under varying signal chaos conditions without subjective impression.

Study Design: Voice signals were constructed with differing degrees of noise to model signal chaos. Within each noise power, 100 Monte Carlo experiments were applied to analyze the output of jitter, shimmer, correlation dimension, and spectrum convergence ratio.

Heat conduction, and the lack thereof, in time-reversible dynamical systems: generalized Nosé-Hoover oscillators with a temperature gradient.

We use nonequilibrium molecular dynamics to analyze and illustrate the qualitative differences between the one-thermostat and two-thermostat versions of equilibrium and nonequilibrium (heat-conducting) harmonic oscillators. Conservative nonconducting regions can coexist with dissipative heat conducting regions in phase space with exactly the same imposed temperature field.

The role of depth and 1/f dynamics in perceiving reversible figures.

When confronted with a reversible figure, such as the Necker Cube, viewers experience a spontaneously changing percept. We assess the dynamic of how the human visual system resolves perceptual ambiguity in stimuli that offer multiple interpretations. Subjects observed the Necker cube for one of three viewing durations during which they pressed a key each time they perceived a change in the orientation of the cube.

Substance abuse as a dynamical disease: evidence and clinical implications of nonlinearity in a time series of daily alcohol consumption.

Several authors have suggested that chaos theory, the study of nonlinear dynamics and the application of the knowledge gained to natural and social phenomena, might yield insight into substance-related disorders. In this article, we examine the dynamics of substance abuse by fitting a nonlinear model to a time series of the amount of alcohol, which an adult male with a diagnosis of substance abuse consumed on a daily basis. The nonlinear model shows a statistically superior fit when compared to a linear model.