Liapunov exponents from a time series of acoustic chaos

The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis

In many countries in Asia and South-America dengue fever (DF) and dengue hemorrhagic fever (DHF) has become a substantial public health concern leading to serious social-economic costs. Mathematical models describing the transmission of dengue viruses have focussed on the so-called antibody-dependent enhancement (ADE) effect and temporary cross-immunity trying to explain the irregular behavior of dengue epidemics by analyzing available data. However, no systematic investigation of the possible dynamical structures has been performed so far. Our study focuses on a seasonally forced (non-autonomous) model with temporary cross-immunity and possible secondary infection, motivated by dengue fever epidemiology. The notion of at least two different strains is needed in a minimalistic model to describe differences between primary infections, often asymptomatic, and secondary infection, associated with the severe form of the disease. We extend the previously studied non-seasonal (autonomous) model by adding seasonal forcing, mimicking the vectorial dynamics, and a low import of infected individuals, which is realistic in the dynamics of dengue fever epidemics. A comparative study between three different scenarios (non-seasonal, low seasonal and high seasonal with a low import of infected individuals) is performed. The extended models show complex dynamics and qualitatively a good agreement between empirical DHF monitoring data and the obtained model simulation. We discuss the role of seasonal forcing and the import of infected individuals in such systems, the biological relevance and its implications for the analysis of the available dengue data. At the moment only such minimalistic models have a chance to be qualitatively understood well and eventually tested against existing data. The simplicity of the model (low number of parameters and state variables) offer a promising perspective on parameter values inference from the DHF case notifications.

Chaos in Voice, From Modeling to Measurement

Chaos has been observed in turbulence, chemical reactions, nonlinear circuits, the solar system, biological populations, and seems to be an essential aspect of most physical systems. Chaos may also be central to the interpretation of irregularity in voice disorders. This presentation will summarize the results from a series of our recent studies. These studies have demonstrated the prescence of chaos in computer models of vocal folds, experiments with excised larynges, and human voices. Methods based on nonlinear dynamics can be used to quantify chaos and irregularity in vocal fold vibration. Studies have suggested that disordered voices from laryngeal pathologies such as laryngeal paralysis, vocal polyps, and vocal nodules might exhibit chaotic behaviors. Conventional parameters, such as jitter and shimmer, may be unreliable for analysis of periodic and chaotic voice signals. Nonlinear dynamic methods, however, have differentiated between normal and pathological phonations and can describe the aperiodic or chaotic voice. Chaos theory and nonlinear dynamics can enchance our understanding and therefore our assessment of pathological phonation.

Comparison of nonlinear dynamic methods and perturbation methods for voice analysis

Nonlinear dynamic methods and perturbation methods are compared in terms of the effects of signal length, sampling rate, and noise. Results of theoretical and experimental studies quantitatively show that measurements representing frequency and amplitude perturbations are not applicable to chaotic signals because of difficulties in pitch tracking and sensitivity to initial state differences. Perturbation analyses are only reliable when applied to nearly periodic voice samples of sufficiently long signal lengths that were obtained at high sampling rates and low noise levels. In contrast, nonlinear dynamic methods, such as correlation dimension, allow the quantification of chaotic time series. Additionally, the correlation dimension method presents a more stable analysis of nearly periodic voice samples for shorter signal lengths, lower sampling rates, and higher noise levels. The correlation dimension method avoids some of the methodological issues associated with perturbation methods, and may potentially improve the ability for real time analysis as well as reduce costs in experimental designs for objectively assessing voice disorders.

Prediction of long-term dynamics from transients

Existing methods of time series analysis of nonlinear dynamical systems deal with the dynamics on single (strange) attractors. We extend this method for systems that can be externally manipulated. We interact with a previously unknown system by perturbing it randomly and recording the responses. By following transients for a short time and approximating the global flow, we can predict the final long-term dynamics, including coexisting multistable, chaotic, or periodic dynamics. Also the localization of basins of attraction is possible, enabling the selection or control of the type of final dynamics. Numerical and experimental examples of driven nonlinear oscillators are given.

Nonlinear dynamics of phonations in excised larynx experiments

Nonlinear dynamic methods including correlation dimension and Lyapunov exponents are applied to quantitatively analyze phonations in excised larynx experiments. Irregular phonations are typically characterized by aperiodic waveforms and broadband spectra. Finite correlation dimensions and positive Lyapunov exponents of irregular phonations demonstrate the existence of chaos in excised larynx phonations. Furthermore, the correlation dimension, maximal Lyapunov exponent, jitter, shimmer, and peak prominence ratio are used to statistically distinguish irregular phonations from normal phonations. The correlation dimension and maximal Lyapunov exponent indicate a significant difference between irregular and normal phonations; however, jitter, shimmer, and peak prominence ratio do not reveal such a significant difference and thus are unsuitable to differentiate between irregular phonations and normal phonations. These findings might potentially assist investigators in understanding rough phonations and developing clinically valuable methodologies for the diagnosis of voice disorders.

Direct observation of period-doubled nonspherical states in single-bubble sonoluminescence

We present direct observations of period doubling in the flash to flash pulse heights in single-bubble sonoluminescence. States involved are stable, spherically symmetry broken. Observations are made using seven detectors distributed in the equatorial plane of the bubble. Contrary to earlier experiments by Holt et al. [Phys. Rev. Lett. 72, 1376 (1994)], where period doubling was observed in the time intervals between flashes but not in the pulse heights, we observe period doubling in pulse heights, but no corresponding period doubling is seen in the time intervals. In parameter space the period doubling is observed below the n=2 shape instability boundary line where extinction is shown to take place.

Stable nonspherical bubble collapse including period doubling in sonoluminescence

We present observations of stable spherical symmetry broken states in single bubble sonoluminescence including observations of period doubled states. States observed involve both spatially oriented states and states with a tumbling symmetry axis. The observations are made using a fiber based four-channel correlation scheme. The measurements are made both with and without narrow band optical filters. The symmetry broken states are seen in all cases even using a 650+/-40-nm filter. This fact may be used to distinguish between different theories for the light emission. Prior to the measurements reported here, theoretical attempts to explain observations of period doubling bifurcation phenomena in single bubble sonoluminescence were centered on radially bifurcated collapses. The present experiments show unequivocally that the observations are primarily a result of breaking the spherical symmetry in the bubble collapse. Period doubling will at most show up as secondary effects in the total light output, if at all.

Period-doubling bifurcations from breaking the spherical symmetry in sonoluminescence: experimental verification

Using a fiber-based four-channel correlation scheme to investigate spatial and temporal correlations, we show that observations of period-doubling phenomena in single bubble sonoluminescence are primarily a result of spontaneously breaking the spherical symmetry in the bubble collapse and, at most, may show up as secondary effects in the flash-to-flash spatially integrated light output.

Modeling of chaotic vibrations in symmetric vocal folds

The chaos mechanism of above-range phonation was examined in symmetrically modeled vocal folds by using the traditional two-mass model assumption. The Poincaré map technique was used to display chaotic attractors. This method provided an effective description of irregular vocal-fold movements. The power spectrum, Lyapunov exponent, and Kaplan-Yorke dimension were employed to describe chaotic vibrations in the vocal-fold model. These nonlinear dynamic analyses suggested that, for the positive Lyapunov exponent, chaotic attractors contribute to irregular vocal-fold vibrations. Descriptions of complicated irregular vibrations of the vocal fold yielded evidence of chaos. To investigate the effects of independent parameters such as subglottal pressure, coupling stiffness, and phonation neutral area, bifurcation diagrams based on the Poincaré map were discussed. The results confirmed that the dynamics of the two-mass model was strongly influenced by independent parameters. Nonlinear dynamic methods were expected to provide useful information for better understanding of irregular vocal-fold vibrations as well as of the dynamic mechanism of above-range phonation in excised larynx experimentation.