arXiv subjects

K. P. Harikrishnan

Publications and source records attributed to K. P. Harikrishnan.

18 recordsLinked to original sources

arXiv2022

Recurrence measures and transitions in stock market dynamics

The financial markets are understood as complex dynamical systems whose dynamics is analysed mostly using nonstationary and brief data sets that usually come from stock markets. For such data sets, a reliable method of analysis is based on recurrence plots and recurrence networks, constructed from the data sets over the period of study. In this study, we do a comprehensive analysis of the complexity of the underlying dynamics of 26 markets around the globe using recurrence based measures. We also examine trends in the nature of transitions as revealed from these measures by the sliding window analysis along the time series during the global financial crisis of 2008 and compare that with changes during the most recent pandemic related lock down. We show that the measures derived from recurrence patterns can be used to capture the nature of transitions in stock market dynamics. Our study reveals that the changes around 2008 indicate stochasticity driven transition, which is different from the transition during the pandemic.

q-fin.ST↗

arXiv2019

Quantifying information loss on chaotic attractors through recurrence networks

We propose an entropy measure for the analysis of chaotic attractors through recurrence networks which are un-weighted and un-directed complex networks constructed from time series of dynamical systems using specific criteria. We show that the proposed measure converges to a constant value with increase in the number of data points on the attractor (or the number of nodes on the network) and the embedding dimension used for the construction of the network, and clearly distinguishes between the recurrence network from chaotic time series and white noise. Since the measure is characteristic to the network topology, it can be used to quantify the information loss associated with the structural change of a chaotic attractor in terms of the difference in the link density of the corresponding recurrence networks. We also indicate some practical applications of the proposed measure in the recurrence analysis of chaotic attractors as well as the relevance of the proposed measure in the context of the general theory of complex networks.

physics.soc-ph↗

arXiv2018

Higher order spectral analysis of ECG signals

Higher Order Spectral (HOS) analysis is often applied effectively to analyze many bio-medical signals to detect nonlinear and non-Gaussian processes. One of the most basic HOS methods is the bispectral estimation, which extracts the degree of quadratic phase coupling between individual frequency components of a nonlinear signal. Most of the studies in this direction as applied to ECG signals are on the conventional, long duration (up to 24 hours) Heart Rate Variability (HRV) data. We report results of our studies on short duration ECG data of 60 seconds using power spectral and bispectral parameters. We analyze 60 healthy cases and 60 cases of patients diagnosed with four different heart diseases, Bundle Branch Block, Cardiomyopathy, Dysrhythmia and Myocardial Infarction. From the power spectra of these data sets we observe that the pulse frequency around 1 Hz has maximum power for all normal ECG data while in all disease cases, the power in the pulse frequency is suppressed and gets distributed among higher frequencies. The bicoherence indices computed show that the pulse frequency has strong quadratic phase coupling with a large number of higher frequencies in healthy cases indicating nonlinearity in the underlying dynamical processes. The loss or decrease of the phase coupling with pulse frequency is a clear indicator of abnormal conditions. In specific cases, bicoherence studies coupled with spectral filter, suggest ECG for Myocardial Infarction has noisy components while in Dysrhythmia, power is mostly at high frequencies with strong quadratic coupling indicating much more irregularity and complexity than normal ECG signals. In addition to serving as indicators suggestive of abnormal conditions of the heart, the detailed analysis presented can lead to a wholistic understanding of normal heart dynamics and its variations during onset of diseases.

physics.med-ph↗

arXiv2017

Degree weighted recurrence networks for the analysis of time series data

Recurrence networks are powerful tools used effectively in the nonlinear analysis of time series data. The analysis in this context is done mostly with unweighted and undirected complex networks constructed with specific criteria from the time series. In this work, we propose a novel method to construct "weighted recurrence network"(WRN) from a time series and show how it can reveal useful information regarding the structure of a chaotic attractor, which the usual unweighted recurrence network cannot provide. Especially, we find the node strength distribution of the WRN, from every chaotic attractor follows a power law (with exponential tail) with the index characteristic to the fractal structure of the attractor. This leads to a new class among complex networks, to which networks from all standard chaotic attractors are found to belong. In addition, we present generalized definitions for clustering coefficient and characteristic path length and show that these measures can effectively discriminate chaotic dynamics from white noise and $1/f$ colored noise. Our results indicate that the WRN and the associated measures can become potentially important tools for the analysis of short and noisy time series from the real world systems as they are clearly demarked from that of noisy or stochastic systems.

nlin.CD↗

arXiv2017

Is a hyperchaotic attractor superposition of two multifractals?

In the context of chaotic dynamical systems with exponential divergence of nearby trajectories in phase space, hyperchaos is defined as a state where there is divergence or stretching in at least two directions during the evolution of the system. Hence the detection and characterization of a hyperchaotic attractor is usually done using the spectrum of Lyapunov Exponents (LEs) that measure this rate of divergence along each direction. Though hyperchaos arise in different dynamical situations and find several practical applications, a proper understanding of the geometric structure of a hyperchaotic attractor still remains an unsolved problem. In this paper, we present strong numerical evidence to suggest that the geometric structure of a hyperchaotic attractor can be characterized using a multifractal spectrum with two superimposed components. In other words, apart from developing an extra positive LE, there is also a structural change as a chaotic attractor makes a transition to the hyperchaotic phase and the attractor changes from a simple multifractal to a dual multifractal, equivalent to two inter-mingled multifractals. We argue that a cross-over behavior in the scaling region for computing the correlation dimension is a manifestation of such a structure. In order to support this claim, we present an illustrative example of a synthetically generated set of points in the unit interval (a Cantor set with a variable iteration scheme) displaying dual multifractal spectrum. Our results are also used to develop a general scheme to generate both hyperchaotic as well as high dimensional chaotic attractors by coupling two low dimensional chaotic attractors and tuning a time scale parameter.

nlin.CD↗

arXiv2017

Recurrence network measures for hypothesis testing using surrogate data: application to black hole light curves

Recurrence networks and the associated statistical measures have become important tools in the analysis of time series data. In this work, we test how effective the recurrence network measures are in analyzing real world data involving two main types of noise, white noise and colored noise. We use two prominent network measures as discriminating statistic for hypothesis testing using surrogate data for a specific null hypothesis that the data is derived from a linear stochastic process. We show that the characteristic path length is especially efficient as a discriminating measure with the conclusions reasonably accurate even with limited number of data points in the time series. We also highlight an additional advantage of the network approach in identifying the dimensionality of the system underlying the time series through a convergence measure derived from the probability distribution of the local clustering coefficients. As examples of real world data, we use the light curves from a prominent black hole system and show that a combined analysis using three primary network measures can provide vital information regarding the nature of temporal variability of light curves from different spectroscopic classes.

physics.data-an↗

arXiv2017

Detecting abnormality in heart dynamics from multifractal analysis of ECG signals

The characterization of heart dynamics with a view to distinguish abnormal from normal behavior is an interesting topic in clinical sciences. Here we present an analysis of the Electro-cardiogram (ECG) signals obtained under controlled conditions from several healthy and unhealthy subjects using the framework of multifractal analysis. Our analysis differs from the conventional nonlinear analysis in that the information contained in the amplitude variations of the signal is being extracted and quantified. The results thus obtained reveal that the attractor underlying the dynamics of the heart has multifractal structure and the resultant multifractal spectra can clearly separate healthy subjects from unhealthy ones. We use supervised machine learning approach to build a model that predicts the group label of a new subject with very high accuracy on the basis of the multifractal parameters. By comparing the range of scaling indices in the multifractal spectra with that of beat replicated data from the same ECG, we show how each ECG can be checked for abnormality for variations within itself.

q-bio.TO↗

arXiv2017

Determining the minimum embedding dimension for state space reconstruction through recurrence networks

The analysis of observed time series from nonlinear systems is usually done by making a time-delay reconstruction to unfold the dynamics on a multi-dimensional state space. An important aspect of the analysis is the choice of the correct embedding dimension. The conventional procedure used for this is either the method of false nearest neighbors or the saturation of some invariant measure, such as, correlation dimension. Here we examine this issue from a complex network perspective and propose a recurrence network based measure to determine the acceptable minimum embedding dimension to be used for such analysis. The measure proposed here is based on the well known Kullback-Leibler divergence commonly used in information theory. We show that the measure is simple and direct to compute and give accurate result for short time series. To show the significance of the measure in the analysis of practical data, we present the analysis of two EEG signals as examples.

q-bio.NC↗

arXiv2016

Measure for degree heterogeneity in complex networks and its application to recurrence network analysis

We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all types of network topology with ease and increases with the diversity of node degrees in the network. The measure is applied to compute the heterogeneity of synthetic (both random and scale free) and real world networks with its value normalized in the interval [0, 1]. To define the measure, we introduce a limiting network whose heterogeneity can be expressed analytically with the value tending to 1 as the size of the network N tends to infinity. We numerically study the variation of heterogeneity for random graphs (as a function of p and N) and for scale free networks with and N as variables. Finally, as a specific application, we show that the proposed measure can be used to compare the heterogeneity of recurrence networks constructed from the time series of several low dimensional chaotic attractors9thereby providing a single index to compare the structural complexity of chaotic attractors.

physics.soc-ph↗

arXiv2016

Can recurrence networks show small world property?

Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value εchosen at or just above the percolation threshold of the network are quite well understood, what happens as the threshold increases beyond the usual operational window is still not clear from a complex network perspective. The present Letter is focused mainly on the network properties at intermediate-to-large values of the recurrence threshold, for which no systematic study has been performed so far. We argue, with numerical support, that recurrence networks constructed from chaotic attractors with εequal to the usual recurrence threshold or slightly above cannot, in general, show small-world property. However, if the threshold is further increased, the recurrence network topology initially changes to a small-worldstructure and finally to that of a classical random graph as the threshold approaches the size of the strange attractor.

nlin.CD↗

arXiv2016

Uniform framework for the recurrence-network analysis of chaotic time series

We propose a general method for the construction and analysis of unweighted $ε$ - recurrence networks from chaotic time series. The selection of the critical threshold $ε_c$ in our scheme is done empirically and we show that its value is closely linked to the embedding dimension $M$. In fact, we are able to identify a small critical range $Δε$ numerically that is approximately the same for the random and several standard chaotic time series for a fixed $M$. This provides us a uniform framework for the non subjective comparison of the statistical measures of the recurrence networks constructed from various chaotic attractors. We explicitly show that the degree distribution of the recurrence network constructed by our scheme is characteristic to the structure of the attractor and display statistical scale invariance with respect to increase in the number of nodes $N$. We also present two practical applications of the scheme, detection of transition between two dynamical regimes in a time delayed system and identification of the dimensionality of the underlying system from real world data with limited number of points, through recurrence network measures. The merits, limitations and the potential applications of the proposed method have also been highlighted.

nlin.CD↗

arXiv2015

How does noise affect the structure of a chaotic attractor: A recurrence network perspective

We undertake a preliminary numerical investigation to understand how the addition of white and colored noise to a time series affects the topology and structure of the underlying chaotic attractor. We use the methods and measures of recurrence networks generated from the time series for this analysis. We explicitly show that the addition of noise destroys the recurrence of trajectory points in the phase space. By using the results obtained from this analysis, we go on to analyse the light curves from a dominant black hole system and show that the recurrence network measures are effective in the analysis of real world data involving noise and are capable of identifying the nature of noise contamination in a time series.

physics.data-an↗

arXiv2010

Nonlinear time series anaysis of the light curves from the black hole system GRS1915+105

GRS 1915+105 is a prominent black hole system exhibiting variability over a wide range of time scales and its observed light curves have been classified into 12 temporal states. Here we undertake a complete analysis of these light curves from all the states using various quantifiers from nonlinear time series analysis, such as, the correlation dimension (D_2), the correlation entropy (K_2), singular value decomposition (SVD) and the multifractal spectrum ($f(α)$ spectrum). An important aspect of our analysis is that, for estimating these quantifiers, we use algorithmic schemes which we have proposed recently and tested successfully on synthetic as well as practical time series from various fields. Though the schemes are based on the conventional delay embedding technique, they are automated so that the above quantitative measures can be computed using conditions prescribed by the algorithm and without any intermediate subjective analysis. We show that nearly half of the 12 temporal states exhibit deviation from randomness and their complex temporal behavior could be approximated by a few (3 or 4) coupled ordinary nonlinear differential equations. These results could be important for a better understanding of the processes that generate the light curves and hence for modelling the temporal behavior of such complex systems. To our knowledge, this is the first complete analysis of an astrophysical object (let alone a black hole system) using various techniques from nonlinear dynamics.

astro-ph.HE↗

arXiv2009

Computing the multifractal spectrum from time series: An algorithmic approach

We show that the existing methods for computing the f(α) spectrum from a time series can be improved by using a new algorithmic scheme. The scheme relies on the basic idea that the smooth convex profile of a typical f(α) spectrum can be fitted with an analytic function involving a set of four independent parameters. While the standard existing schemes [16, 18] generally compute only an incomplete f(α) spectrum (usually the top portion), we show that this can be overcome by an algorithmic approach which is automated to compute the Dq and f(α) spectrum from a time series for any embedding dimension. The scheme is first tested with the logistic attractor with known f(α) curve and subsequently applied to higher dimensional cases. We also show that the scheme can be effectively adapted for analysing practcal time series involving noise, with examples from two widely different real world systems. Moreover, some preliminary results indicating that the set of four independant parameters may be used as diagnostic measures is also included.

nlin.CD↗

arXiv2007

Resonance phenomena in discrete systems with bichromatic input signal

We undertake a detailed numerical study of the twin phenomena of stochastic and vibrational resonance in a discrete model system in the presence of bichromatic input signal. A two parameter cubic map is used as the model that combines the features of both bistable and threshold settings. Our analysis brings out several interesting results, such as, the existence of a cross over behaviour from vibrational to stochastic resonance and the possibility of using stochastic resonance as a filter for the selective detection/transmission of the component frequencies in a composite signal. The study also reveals a fundamental difference between the bistable and threshold mechanisms with respect to amplification of a multi signal input.

nlin.CD↗

arXiv2006

The non-linear behavior of the black hole system GRS 1915+105

Using non-linear time series analysis, along with surrogate data analysis, it is shown that the various types of long term variability exhibited by the black hole system GRS 1915+105, can be explained in terms of a deterministic non-linear system with some inherent stochastic noise. Evidence is provided for a non-linear limit cycle origin of one of the low frequency QPO detected in the source, while some other types of variability could be due to an underlying low dimensional chaotic system. These results imply that the partial differential equations which govern the magneto-hydrodynamic flow of the inner accretion disk, can be approximated by a small number ($\approx 3 -5$) of non-linear but {\it ordinary} differential equations. While this analysis does not reveal the exact nature of these approximate equations, they may be obtained in the future, after results of magneto-hydrodynamic simulation of realistic accretion disks become available.

astro-ph↗

arXiv2006

A non subjective approach to the GP algorithm for analysing noisy time series

We present an adaptation of the standard Grassberger-Proccacia (GP) algorithm for estimating the Correlation Dimension of a time series in a non subjective manner. The validity and accuracy of this approach is tested using different types of time series, such as, those from standard chaotic systems, pure white and colored noise and chaotic systems added with noise. The effectiveness of the scheme in analysing noisy time series, particularly those involving colored noise, is investigated. An interesting result we have obtained is that, for the same percentage of noise addition, data with colored noise is more distinguishable from the corresponding surrogates, than data with white noise. As examples for real life applications, analysis of data from an astrophysical X-ray object and human brain EEG, are presented.

nlin.CD↗

arXiv2004

The chaotic behavior of the black hole system GRS 1915+105

A modified non-linear time series analysis technique, which computes the correlation dimension $D_2$, is used to analyze the X-ray light curves of the black hole system GRS 1915+105 in all twelve temporal classes. For four of these temporal classes $D_2 $ saturates to $\approx 4-5$ which indicates that the underlying dynamical mechanism is a low dimensional chaotic system. Of the other eight classes, three show stochastic behavior while five show deviation from randomness. The light curves for four classes which depict chaotic behavior have the smallest ratio of the expected Poisson noise to the variability ($ < 0.05$) while those for the three classes which depict stochastic behavior is the highest ($ > 0.2$). This suggests that the temporal behavior of the black hole system is governed by a low dimensional chaotic system, whose nature is detectable only when the Poisson fluctuations are much smaller than the variability.

astro-ph↗