arXiv subjects

G. Ambika

Publications and source records attributed to G. Ambika.

67 records · Page 4Linked to original sources

arXiv2011

On interrelations of recurrences and connectivity trends between stock indices

Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient ρ as the point of departure. We employ an estimator based on recurrence plots --- the Correlation of Probability of Recurrence (CPR) --- to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the CPR approach in order to get more robust results. We examine trends in CPR for an approximately 19-month window moved along the time series and compare them to ρ. Binning CPR into three levels of connectedness: strong, moderate and weak, we extract the trends in number of connections in each bin over time. We also look at the behavior of CPR during the Dot-Com bubble by shifting the time series to align their peaks. CPR mainly uncovers that the markets move in and out of periods of strong connectivity erratically, instead of moving monotonously towards increasing global connectivity. This is in contrast to ρ, which gives a picture of ever increasing correlation. CPR also exhibits that time shifted markets have high connectivity around the Dot-Com bubble of 2000. We stress on the importance of significance testing in interpreting measures applied to field data. CPR is more robust to significance testing. It has the additional advantages of being robust to noise, and reliable for short time series lengths and low frequency of sampling. Further, it is more sensitive to changes than ρ as it captures correlations between the essential dynamics of the underlying systems.

q-fin.ST↗

arXiv2010

Neuronal networks with coupling through amyloid beta: towards a theory for Alzheimer's disease

Alzheimer's disease (AD) is a common form of dementia observed in the elderly due to neurodegenerative disorder and dysfunction. This arises from alterations in synaptic functioning of neurons leading to cognitive impairment and memory loss. Recent experimental studies indicate that the amyloid beta (A beta) protein, in its dimer and oligomer forms, affects the synaptic activity of neurons in the early stages of AD. However, the precise mechanism underlying A beta induced synaptic depression is still not clearly understood. In this paper, we introduce an electrical model that provides a possible mechanism for this. Our studies show that the competing effects of synaptic activity and the indirect interaction mediated by A beta, can disrupt the synchrony among neurons and severely affect the neuronal activity. This then leads to sub-threshold activity or synaptic silencing. This is in agreement with the reported disruption of cortical synaptic integration in the presence of A beta in transgenic mice. We suggest that direct electrophysiological measurements of A beta activity can establish its role in AD and the possible revival, proposed in our model. The mechanism proposed here is quite general and could account for the role of the relevant protein in other neuronal disorders also.

q-bio.NC↗

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↗

arXiv2010

Synchronization of time delay systems using variable delay with reset for enhanced security in communication

We have introduced a mechanism for synchronizing chaotic systems by one way coupling with a variable delay that is reset at finite intervals. Here we extend this method to time delay systems and suggest a new cryptosystem based on this. We present the stability analysis as applied to time delay systems and supplement this by numerical simulations in a standard time delay system like Mackey Glass system. We extend the theory to multi- delay systems and propose a bi channel scheme for the implementation of the scheme for communication with enhanced security. We show that since the synchronizing channel carries information from transmitter only at intervals of reset time, it is not susceptible to reconstruction. The message channel being separate can be made complex by linear combination of transmitter variable at different delay times using mutiple delay systems. This method has the additional advantage that it can be adjusted to be delay or anticipatory in synchronization and these provide two additional basic keys that are independent of system delay.

nlin.CD↗

arXiv2010

Synchronized states in chaotic systems coupled indirectly through a dynamic environment

We consider synchronization of chaotic systems coupled indirectly through a common environmnet where the environment has an intrinsic dynmics of its own modulated via feedback from the systems. We find that a rich vareity of synchronization behavior, such as in-phase, anti-phase,complete and anti- synchronization is possible. We present an approximate stability analysis for the different synchronization behaviors. The transitions to different states of synchronous behaviour are analyzed in the parameter plane of coupling strengths by numerical studies for specific cases such as Rossler and Lorenz systems and are characterized using various indices such as correlation, average phase difference and Lyapunov exponents. The threshold condition obtained from numerical analysis is found to agree with that from the stability analysis.

nlin.CD↗

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↗

arXiv2008

Antiphase Synchronization in Environmentally coupled Rossler Oscillators

We study the manifestation of antiphase synchronization in a system of n Rossler Oscillators coupled through a dynamic environment. When the feedback from system to environment is positive (negative) and that from environment to system is negative (positive), the oscillators enter into a state of anti phase synchronization both in periodic and chaotic regimes. Their phases are found to be uniformly distributed over 2$pi$, with a phase lag of 2$pi$ /n between neighbors as is evident from the similarity function and the phase plots. The transition to anti phase synchronization is marked by the crossover of (n-1) zero Lyapunov Exponents to negative values. If the systems are individually in chaotic phase, with strong enough coupling they end up in periodic states which are in antiphase synchronization

nlin.CD↗

arXiv2008

Anticipatory synchronization with variable time delay and reset

A method to synchronize two chaotic systems with anticipation or lag, coupled in the drive response mode, is proposed. The coupling involves variable delay with three time scales. The method has the advantage that synchronization is realized with intermittant information about the driving system at intervals fixed by a reset time. The stability of the synchronization manifold is analyzed with the resulting discrete error dynamics. The numerical calculations in standard systems like the Rossler and Lorenz systems are used to demonstrate the method and the results of the analysis.

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↗

arXiv2000

Bubbling and bistability in two parameter discrete systems

We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis is that whether it is bubbling or bistability is decided by the sign of the third derivative at the inflection point of the map function.

nlin.CD↗