arXiv subjects

A. N. Sekar Iyengar

Publications and source records attributed to A. N. Sekar Iyengar.

At least 19 recordsLinked to original sources

arXiv2020

Fractal dimension analysis of spatio-temporal patterns using image processing and nonlinear time-series analysis

This article deals with the estimation of fractal dimension of spatio-temporal patterns that are generated by numerically solving the Swift Hohenberg (SH) equation. The patterns were converted into a spatial series (analogous to time series) which were shown to be chaotic by evaluating the largest Lyapunov exponent. We have applied several nonlinear time-series analysis techniques like Detrended fluctuation and Rescaled range on these spatial data to obtain Hurst exponent values that reveal spatial series data to be long range correlated. We have estimated fractal dimension from the Hurst and power law exponent and found the value lying between 1 and 2. The novelty of our approach lies in estimating fractal dimension using image to data conversion and spatial series analysis techniques, crucial for experimentally obtained images.

nlin.PS↗

arXiv2017

Interplay of transitions between oscillations with emergence of fireballs and quantification of phase coherence, scaling index in a magnetized glow discharge plasma of toroidal assembly

Interplay of transition of floating potential fluctuations in a glow discharge plasma in the toroidal vacuum vessel of SINP tokamak has been observed. With variation in the strength of the vertical and toroidal magnetic fields, regular and inverted relaxation oscillations as well as sinusoidal oscillations are observed with the slow and fast time scale of the relaxation oscillations reversing their nature at a high value of vertical magnetic field strength. However for small value of toroidal magnetic field the transitions follow relaxation $\rightarrow$ chaotic oscillations with the chaotic nature prevailing at higher values of toroidal magnetic field. Evolution of associated anode fireball dynamics under the action of increasing vertical, toroidal as well as increasing vertical field at a fixed toroidal field (mixed field) of different strength has been studied. Estimation of phase coherence index for each case has been carried out to examine the evidence of finite nonlinear interaction. A comprehensive study of the dynamics of the fireball is found to be associated with the values of phase coherence index. The index is found to take maximum values for the case of toroidal, mixed field when there is an existence of power/energy concentration in a large region of frequency band. A detailed study of the scaling region using detrended fluctuation analysis (DFA) by estimating the scaling exponent has been carried out for increasing values of discharge voltage, vertical, toroidal as well as the mixed field (toroidal plus vertical). A persistence long range behaviour associated with the nature of the anode glow has been investigated in case of higher values of toroidal, mixed field whereas increasing DV, vertical magnetic field leads to a perfectly correlated dynamics with values of scaling exponent greater than unity

physics.plasm-ph↗

arXiv2017

Quantification of scaling exponent with crossover type phenomena for different types of forcing in DC glow discharge plasma

We have carried out a detailed study of scaling region using detrended fractal analysis test by applying different forcing likewise noise, sinusoidal, square on the floating potential fluctuations acquired under different pressures in a DC glow discharge plasma. The transition in the dynamics is observed through recurrence plot techniques which is an efficient method to observe the critical regime transitions in dynamics. The complexity of the nonlinear fluctuation has been revealed with the help of recurrence quantification analysis which is a suitable tool for investigating recurrence, an ubiquitous feature providing a deep insight into the dynamics of real dynamical system. An informal test for stationarity which checks for the compatibility of nonlinear approximations to the dynamics made in different segments in a time series has been proposed. In case of sinusoidal, noise, square forcing applied on fluctuation acquired at P=0.12mbar only one dominant scaling region is observed whereas the forcing applied on fluctuation (P=0.004mbar) two prominent scaling regions have been explored reliably using different forcing amplitudes indicating the signature of crossover phenomena. Furthermore a persistence long range behaviour has been observed in one of these scaling regions. A comprehensive study of the quantifi- cation of scaling exponents has been carried out with the increase in amplitude and frequency of sinusoidal, square type of forcings. The scalings exponent is envisaged to be the roughness of the time series. The method provides a single quantitative idea of the scaling exponent to quantify the correlation properties of a signal.

physics.data-an↗

arXiv2017

Effect of magnetic field on the hysteresis phenomena and floating potential oscillations in a reflex plasma source

An experimental investigation on the periodic and chaotic oscillations in a reflex plasma source in presence of magnetic field is presented. The experiment is conducted in a reflex plasma source, consisting of two cathodes and a ring anode. A penning type DC glow discharge in an uniform axial magnetic field is initiated in the background of argon gas. The current-voltage characteristics near the breakdown voltage show a hysteresis with two distinct discharge current regimes. The effect of magnetic field on the discharge current and floating potential oscillations is studied when the discharge is operated within this hysteresis loop. At a typical axial magnetic field, the discharge transits from high discharge current regime (beyond 4-5 mA), an oscillation free regime, to a low discharge current regime (less than 1 mA). Depending upon the discharge parameters, low discharge current regime shows either the periodic or chaotic oscillation in the frequency range of 1-50 KHz. The frequency of periodic oscillation increases with the increase in magnetic field up to 90 Gauss and with further increase in magnetic field, the periodic oscillation becomes chaotic in nature.

physics.plasm-ph↗

arXiv2016

Self-organised-criticality and punctuated equilibrium in bouncing balls

A nonlinearly coupled system of bouncing balls is shown to exhibit features like self-organised-criticality (SOC) and punctuated equilibrium (PE) in suitable parameter domains. The temporal evolution of the non-stationary amplitudes is analysed through local methods to unravel the transient periodic components and fluctuations giving rise to SOC and PE type behaviours. This simple dynamical system follows Gutenberg-Richter relation and also manifests the Devil's staircase, explicating the universality of these features in diverse complex systems.

nlin.CD↗

arXiv2014

Investigation of stochastic resonance (SR) near homoclinic bifurcation in a unijunction transistor (UJT) relaxation oscillator

A P-spice simulation followed by an experiment with a unijunction transistor (UJT) has been carried out to investigate stochastic resonance (SR) in which the response of a nonlinear system to a weak periodic input signal is amplified by an optimum level of noise. The experiments were carried out in the vicinity of homoclinic bifurcation and the quantification of SR has been done by normal variance (NV) and signal to noise ratio (SNR) techniques. We have also developed a tentative mathematical model based on the current-voltage characteristic of the UJT and obtained a second order differential equation that was solved using MATLAB to yield a response similar to the one observed experimentally.

nlin.AO↗

arXiv2014

Canard-induced mixed mode oscillations in an excitable glow discharge plasmas

We demonstrated experimentally canard induced mixed mode oscillations (MMO) in an excitable glow discharge plasma, and the results are validated through numerical solution of the FitzHugh Nagumo (FHN) model. When glow discharge plasma is perturbed by applying a magnetic field, it shows mixed mode oscillatory activity, i.e., quasiperiodic small oscillations interposed with large bounded limit cycles oscillations. The initial quasiperiodic oscillations were observed to change into large amplitude limit cycle oscillations with magnetic field, and the number of these oscillation increases with increase in the magnetic field. Fourier analysis of both numerical and experimental results show that the origin of these oscillations are canard-induced phenomena, which occurs near the threshold of the control parameter. Further, the phase space plots also confirm that the oscillations are basically canard-induced MMOs.

nlin.CD↗

arXiv2014

Non-stationary Dynamics in the Bouncing Ball: A Wavelet perspective

The non-stationary dynamics of a bouncing ball, comprising of both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signature of self-similarity, complex scaling behavior and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding to neutral turbulence, viscous dissipation regions and different time varying periodic modulations.

math-ph↗

arXiv2014

Multi-scale dynamics of glow discharge plasma through wavelets: Self-similar behavior to neutral turbulence and dissipation

The multiscale dynamics of glow discharge plasma is analysed through wavelet transform, whose scale dependent variable window size aptly captures both transients and non-stationary periodic behavior. The optimal time-frequency localization ability of the continuous Morlet wavelet is found to identify the scale dependent periodic modulations efficiently, as also the emergence of neutral turbulence and dissipation, whereas the discrete Daubechies basis set has been used for detrending the temporal behavior to reveal the multi-fractality of the underlying dynamics. The scaling ex- ponents and the Hurst exponent have been estimated through wavelet based detrended fluctuation analysis,and also Fourier methods and rescale range analysis.

quant-ph↗

arXiv2013

Differential Entropy Dynamics: A Possible Cause of Coherence Resonance

Coherence resonance can be explained using differential entropy and mutual information. This theory explores the role of external noise in stabilising chaotic circuits such as the uni-junction transistor relaxation oscillator.The phenomenon of coherence resonance maximizes differential entropy and mutual information.Thus most natural chaotic oscillators show coherence resonance in the presence of an external driving noise.

nlin.CD↗

arXiv2010

Effect of a sub and supra-threshold periodic forcing an excitable glow discharge plasma near its bifurcation point

In this paper non-linear dynamics of a periodically forced excitable glow discharge plasma has been studied. The experiments were performed in glow discharge plasma where excitability was achieved for suitable discharge voltage and gas pressure. The plasma was first perturbed by a sub-threshold sawtooth periodic signal, and we obtained small sub-threshold oscillations. These oscillations showed resonance when the frequency of the perturbation was around the characteristic frequency the plasma, and hence may be useful to estimate characteristic of an excitable system. On the other hand, when the perturbation was supra-threshold, system showed frequency entrainments. We obtained harmonic frequency entrainments for perturbation frequency greater than the characteristic frequency of the system and for lesser than the characteristic frequency, system showed only excitable behaviour.

nlin.CD↗

arXiv2009

Wavelet Based Volatility Clustering Estimation of Foreign Exchange Rates

We have presented a novel technique of detecting intermittencies in a financial time series of the foreign exchange rate data of U.S.- Euro dollar(US/EUR) using a combination of both statistical and spectral techniques. This has been possible due to Continuous Wavelet Transform (CWT) analysis which has been popularly applied to fluctuating data in various fields science and engineering and is also being tried out in finance and economics. We have been able to qualitatively identify the presence of nonlinearity and chaos in the time series of the foreign exchange rates for US/EURO (United States dollar to Euro Dollar) and US/UK (United States dollar to United Kingdom Pound) currencies. Interestingly we find that for the US-INDIA(United States dollar to Indian Rupee) foreign exchange rates, no such chaotic dynamics is observed. This could be a result of the government control over the foreign exchange rates, instead of the market controlling them.

q-fin.ST↗

arXiv2009

Continuous wavelet transform based time-scale and multi-fractal analysis of the nonlinear oscillations in a hollow cathode glow discharge plasma

Continuous wavelet transform (CWT) based time-scale and multi-fractal analyses have been carried out on the anode glow related nonlinear floating potential fluctuations in a hollow cathode glow discharge plasma. CWT has been used to obtain the contour and ridge plots. Scale shift (or inversely frequency shift) which is a typical nonlinear behaviour, has been detected from the undulating contours. From the ridge plots, we have identified the presence of nonlinearity and degree of chaoticity. Using the wavelet transform modulus maxima technique we have obtained the multi-fractal spectrum for the fluctuations at different discharge voltages and the spectrum was observed to become a monofractal for periodic signals. These multi-fractal spectra were also used to estimate different quantities like the correlation and fractal dimension, degree of multi-fractality and complexity parameters. These estimations have been found to be consistent with the nonlinear time series analysis.

physics.plasm-ph↗

arXiv2009

Comparative study of nonlinear properties of EEG signals of a normal person and an epileptic patient

Background: Investigation of the functioning of the brain in living systems has been a major effort amongst scientists and medical practitioners. Amongst the various disorder of the brain, epilepsy has drawn the most attention because this disorder can affect the quality of life of a person. In this paper we have reinvestigated the EEGs for normal and epileptic patients using surrogate analysis, probability distribution function and Hurst exponent. Results: Using random shuffled surrogate analysis, we have obtained some of the nonlinear features that was obtained by Andrzejak \textit{et al.} [Phys Rev E 2001, 64:061907], for the epileptic patients during seizure. Probability distribution function shows that the activity of an epileptic brain is nongaussian in nature. Hurst exponent has been shown to be useful to characterize a normal and an epileptic brain and it shows that the epileptic brain is long term anticorrelated whereas, the normal brain is more or less stochastic. Among all the techniques, used here, Hurst exponent is found very useful for characterization different cases. Conclusions: In this article, differences in characteristics for normal subjects with eyes open and closed, epileptic subjects during seizure and seizure free intervals have been shown mainly using Hurst exponent. The H shows that the brain activity of a normal man is uncorrelated in nature whereas, epileptic brain activity shows long range anticorrelation.

physics.med-ph↗

arXiv2009

Coherence resonance in an unijunction transistor relaxation oscillator

The phenomenon of coherence resonance (CR) is investigated in an unijunction transistor relaxation oscillator (UJT-RO) and quantified by estimating the normal variance (NV). Depending upon the measuring points two types of NV curves have been obtained. We have observed that the degradations in coherency at higher noise amplitudes in our system is probably the result of direct interference of coherent oscillations and the stochastic perturbation. Degradation of coherency may be minimal if this direct interference of noise and coherent oscillations is eliminated.

nlin.CD↗

arXiv2008

Noise invoked resonances near a homoclinic bifurcation in the glow discharge plasma

Stochastic Resonance (SR) and Coherence Resonance (CR) have been studied experimentally in the discharge plasma close to a homoclinic bifurcation. For the SR phenomena, it is observed that a superimposed subthreshold periodic signal can be recovered via stochastic modulations of the discharge voltage. Furthermore, it is realized that even in the absence of a subthreshold deterministic signal, the system dynamics can be recovered and optimized using noise. This effect is defined as CR in the literature. In the present experiments, induction of SR and CR are quantified using the Absolute Mean Difference (AMD) and Normalized Variance (NV) techniques respectively. AMD is a new statistical tool to quantify regularity in the stochastic resonance and is independent of lag.

physics.plasm-ph↗

arXiv2007

Stochastic behaviour in the edge region of the SINP tokamak

Stochasticity is one of the most extensively researched topics in laboratory and space plasmas since it has been successful in explaining the various anomalous processes like transport, particle heating, particle loss etc. Since there is a growing need for better understanding of this nonlinear process, it has led to the development of new and more advanced data analysis techniques. In this paper we present an analysis of the floating potential fluctuations which show the existence of a stochastic multifractal process along with low dimensional chaos. This has been shown primarily by wavelet analysis, and cross checked using other nonlinear techniques.

physics.plasm-ph↗

arXiv2007

Parametric investigation of nonlinear fluctuations in a dc glow discharge plasma

Glow discharge plasmas exhibit various types of self excited oscillations for different initial conditions like discharge voltages and filling pressures. The behavior of such oscillations associated with the anode glow have been investigated using nonlinear techniques like correlation dimension, largest Lyapunov exponent etc. It is seen that these oscillations go to an ordered state from a chaotic state with increase in input energy i.e. with discharge voltages implying occurrence of inverse bifurcations. These results are different from the other observations wherein the fluctuations have been observed to go from ordered to chaotic state.

physics.plasm-ph↗