arXiv subjects

Rinku Jacob

Publications and source records attributed to Rinku Jacob.

8 recordsLinked to original sources

arXiv2024

Tracking Dynamical Transitions using Link Density of Recurrence Networks

We present Link Density (LD) computed from the Recurrence Network (RN) of a time series data as an effective measure that can detect dynamical transitions in a system. We illustrate its use using time series from the standard Rossler system in the period doubling transitions and the transition to chaos. Moreover, we find that the standard deviation of LD can be more effective in highlighting the transition points. We also consider the variations in data when the parameter of the system is varying due to internal or intrinsic perturbations but at a time scale much slower than that of the dynamics. In this case also, the measure LD and its standard deviation correctly detect transition points in the underlying dynamics of the system. The computation of LD requires minimal computing resources and time, and works well with short data sets. Hence, we propose this measure as a tool to track transitions in dynamics from data, facilitating quicker and more effective analysis of large number of data sets.

physics.data-an↗

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

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

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↗