Non-stationary dynamics in the bouncing ball: A wavelet perspective

Behera, Abhinna; Iyengar, A. N. Sekar; Panigrahi, Prasanta K.

doi:10.1063/1.4896774

Cited by 11 publications

(9 citation statements)

References 48 publications

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“…This is the frequency where the transfer of power occurs at the boundary of low frequency alpha and beta waves that becomes prominent for patients during seizure. We also analyzed the energy transfer phenomenon [37,38], by reconstructing the time series from the Fourier space, excluding the UPO range 8-14Hz for use in the Heisenberg model. Once these characteristic frequencies are removed at 8-14Hz in UPO range, the universal scale free behavior is manifest in the Heisenberg model.…”

Section: Resultsmentioning

confidence: 99%

Evidence of coupled oscillator to wave packet dynamics in human brain

Pal¹,

Neeraj²,

Panigrahi³

2020

Preprint

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Clear evidence of oscillator dynamics to wave packet collapse and revival in the brain EEG signals is demonstrated for the first time, with distinct differences in healthy individuals and epileptic patients. The low frequency components exhibit single oscillator type behavior in a phase-space description, with the potentials as coordinates and their instantaneous changes as the corresponding velocities. The closed paths reveal periodic motion, well described by one linear oscillator or possibly coupled ones with limit cycle dynamics and synchronization at the macroscopic level. The epileptic patients reveal dynamical features of bi-stability, originating from non-linearity, a prominent feature in the signals from the epileptogenic zone and much enhanced during the periods of seizure. Analogy from the phase-space of oscillator dynamics reveals dominance of potential energy in the signals from the epileptogenic zone, as also in the patients during occurrence of seizure. The acceleration, arising from the change of velocity, is found to be particularly strong in epileptic patients, when the phase space shows bi-stability and bursty behavior. Wave behavior with characteristics of superposition emerges in the frequency range corresponding to the observed unstable periodic orbits, that appear at the boundary of alpha and beta waves of 8-14Hz, centered at 10Hz. A modulated carrier wave is observed for all subjects at 18Hz, higher in width for patients. Coherent wave dynamics, with interference playing a key role in the wave packet collapse and revival, is observed starting from 18Hz, with the coherence getting significantly enhanced around 40-45Hz. Mechanism of intra frequency energy transfer is shown to be neutral turbulence.

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Section: Resultsmentioning

confidence: 99%

Evidence of coupled oscillator to wave packet dynamics in human brain

Pal¹,

Neeraj²,

Panigrahi³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…This is the frequency where the transfer of power occurs at the boundary of low frequency alpha and beta waves that becomes prominent for patients during seizure. We also analysed the energy transfer phenomenon [36,37], by reconstructing the time series from the Fourier space, excluding the UPO range 8-14Hz for use in the Heisenberg model. Once these characteristic frequencies are removed at 8-14Hz in UPO range, the universal scale free behaviour is manifest in the Heisenberg model.…”

Section: Resultsmentioning

confidence: 99%

Evidence of wave particle duality in human brain dynamics

Pal

Neeraj

Panigrahi

2020

Preprint

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Clear evidence of wave-particle duality in the brain dynamics is demonstrated for the first time, from the EEG signals of healthy individuals and epileptic patients. The low frequency components exhibit particle type behaviour in a phase-space description, with the potentials as coordinates and their instantaneous changes as the corresponding velocities. The closed paths reveal periodic motion, well described by one linear oscillator or possibly coupled ones with limit cycle dynamics and synchronization at the macroscopic level. The epileptic patients reveal dynamical features of bi-stability, originating from non-linearity, a prominent feature in the signals from the epileptogenic zone and much enhanced during the periods of seizure. Analogy from the phase-space of oscillator dynamics reveals dominance of potential energy in the signals from the epileptogenic zone, as also in the patients during occurrence of seizure. The acceleration, arising from the change of velocity, is found to be particularly strong in epileptic patients, when the phase space shows bi-stability and bursty behaviour. Wave behaviour with characteristics of superposition emerges in the frequency range corresponding to the observed unstable periodic orbits, that appear at the boundary of alpha and beta waves of 8-14Hz, centred at 10Hz. A modulated carrier wave is observed for all subjects at 18Hz, higher in width for patients. Coherent wave dynamics, with interference playing a key role in the wave packet collapse and revival, is observed starting from 18Hz, with the coherence getting significantly enhanced around 40-45Hz. Mechanism of intra frequency energy transfer is shown to be neutral turbulence.

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“…A careful study of CWT coefficients, as shown in Fig.21(a), (b) and (c), reveal that BSE and NYSE are moving in tandem, except when one of them is non-periodic, revealing a transition period leading to an unstable regime [24,41]. Fig.21(c), exhibiting the degree of integration of BSE.…”

Section: Comparing the Coefficients Of Bse And Nysementioning

confidence: 95%

“…As is well known, stock prices are affected by a plethora of factors, the dynamics of which do not get easily revealed in the time series plot of the stock prices [23]. A better understanding of the market dynamics is obtained through phase-space analysis, through the study of the returns as a function of the price indexes, akin to the velocity-trajectory plots in particle dynamics [24,25]. The phase space plots shown in Fig.4, clearly reveal periodic and structured variations, both in the short and long time scales.…”

Section: Datamentioning

confidence: 99%

Causality and correlations between BSE and NYSE indexes: A Janus faced relationship

Neeraj¹,

Panigrahi²

2017

Physica A: Statistical Mechanics and its Applications

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We study the multi-scale temporal correlations and causality connections between the New York Stock Exchange (NYSE) and Bombay Stock Exchange (BSE) monthly average closing price indexes for a period of 300 months, encompassing the time period of the liberalisation of the Indian economy and its gradual global exposure. In multi-scale analysis; clearly identifiable 1, 2 and 3 year non-stationary periodic modulations in NYSE and BSE have been observed, with NYSE commensurating changes in BSE at 3 years scale. Interestingly, at one year time scale, the two exchanges are phase locked only during the turbulent times, while at the scale of three year, in-phase nature is observed for a much longer time frame. The two year time period, having characteristics of both one and three year variations, acts as the transition regime. The normalised NYSE's stock value is found to Granger cause those of BSE, with a time lag of 9 months. Surprisingly, observed Granger causality of high frequency variations reveals BSE behaviour getting reflected in the NYSE index fluctuations, after a smaller time lag. This Janus faced relationship, shows that smaller stock exchanges may provide a natural setting for simulating market fluctuations of much bigger exchanges. This possibly arises due to the fact that high frequency fluctuations form an universal part of the financial time series, and are expected to exhibit similar characteristics in open market economies.

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Non-stationary dynamics in the bouncing ball: A wavelet perspective

Cited by 11 publications

References 48 publications

Evidence of coupled oscillator to wave packet dynamics in human brain

Evidence of coupled oscillator to wave packet dynamics in human brain

Evidence of wave particle duality in human brain dynamics

Causality and correlations between BSE and NYSE indexes: A Janus faced relationship

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