Failure of dimension analysis in a simple five-dimensional system

Jedynak, Andreas; Bach, Michael; Timmer, Jens

doi:10.1103/physreve.50.1770

Cited by 19 publications

(9 citation statements)

References 25 publications

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“…Jedynak et al [38] suggest M$200-1000 for a data set of length N$10 4 -10 6 . Theiler [39] suggests that M=N ¼ 1=3 for optimum precision, although he admits the estimate to be 'shallow' allowing that smaller ratios may produce good results.…”

Section: Correlation Dimensionmentioning

confidence: 99%

On the Use of Attractor Dimension as a Feature in Structural Health Monitoring

Nichols¹,

Virgin²,

Todd

et al. 2003

Mechanical Systems and Signal Processing

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Section: Correlation Dimensionmentioning

confidence: 99%

On the Use of Attractor Dimension as a Feature in Structural Health Monitoring

Nichols¹,

Virgin²,

Todd

et al. 2003

Mechanical Systems and Signal Processing

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“…С другой стороны, может оказаться, что этого числа N недостаточно для корректного определения фрактальной размерности. Известно [6], что N должно быть порядка…”

Section: обоснование основных звеньев предлагаемой информационной теunclassified

New information technology for research of electrical activity of a brain of the man

Polonnikov¹

2014

Тр. СПИИРАН

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“…The surrogate data differs from the tremor voice in that it does not have a scaling region and the slope does not converge with increasing m . The estimated dimension of the tremor voice is significantly less than that of the surrogate data, and thus the results of dimension analysis of the tremor time series can be distinguished from noise data [36,37]. A significant difference between the estimated dimensions for the original and surrogate data can also be found in other tremor voices.…”

Section: Nonlinear Dynamic Analysis Of Pathological Voices From Pamentioning

confidence: 99%

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

Jiang

2008

Journal of Sound and Vibration

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Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show lowdimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.

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Failure of dimension analysis in a simple five-dimensional system

Cited by 19 publications

References 25 publications

On the Use of Attractor Dimension as a Feature in Structural Health Monitoring

On the Use of Attractor Dimension as a Feature in Structural Health Monitoring

New information technology for research of electrical activity of a brain of the man

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

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