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Ramakrishna Ramaswamy

Publications and source records attributed to Ramakrishna Ramaswamy.

At least 19 recordsLinked to original sources
arXiv2021

Phase-locking in $k$-partite networks of delay-coupled oscillators

We examine the dynamics of an ensemble of phase oscillators that are divided in $k$ sets, with time-delayed coupling interactions {\em only} between oscillators in different sets or partitions. The network of interactions thus form a $k-$partite graph. We observe a variety of phase-locked states that include, in addition to the in-phase fully synchronized solution, a variety of splay cluster solutions; all oscillators within a partition are synchronised and the phase differences between oscillators in different partitions are multiples of $2π/k$. Such solutions exist independent of the delay and we determine the generalised stability criteria for the existence of these phase-locked solutions for the $k-$partite system. With increase in time-delay, there is an increase in multistability: the above generic solutions coexist with a number of other partially synchronized solutions. We apply the Ott-Antonsen ansatz for the special case of a symmetric $k-$partite graph to obtain a single time-delayed differential equation for the attracting synchronization manifold. The agreement with numerical results for the specific case of oscillators on a tripartite lattice (the $k=3$ case) is excellent.

nlin.CD↗
arXiv2020

A higher-dimensional generalization of the Lozi map: Bifurcations and dynamics

We generalize the two dimensional Lozi map in order to systematically obtain piece-wise continuous maps in three and higher dimensions. Similar to higher-dimensional generalizations of the related Henon map, these higher-dimensional Lozi maps support hyperchaotic dynamics. We carry out a bifurcation analysis and investigate the dynamics through both numerical and analytical means. The analysis is extended to a sequence of approximations that smooth the discontinuity in the Lozi map.

nlin.CD↗
arXiv2016

A general mechanism for the `$1/f$' noise

We consider the response of a memoryless nonlinear device that converts an input signal $ξ(t)$ into an output $η(t)$ that only depends on the value of the input at the same time, $t$. For input Gaussian noise with power spectrum $1/f^α$, the nonlinearity modifies the spectral index of the output to give a spectrum that varies as $1/f^{α'}$ with $α' \neq α$. We show that the value of $α'$ depends on the nonlinear transformation and can be tuned continuously. This provides a general mechanism for the ubiquitous `$1/f$' noise found in nature.

cond-mat.stat-mech↗
arXiv2016

Emergent organization in a model market

We study the collective behavior of interacting agents in a simple model of market economics originally introduced by Nørrelykke and Bak. A general theoretical framework for interacting traders on an arbitrary network is presented, with the interaction consisting of buying (namely, consumption) and selling (namely, production) of commodities. Extremal dynamics is introduced by having the agent with least profit in the market readjust prices, causing the market to self--organize. We study this model market on regular lattices in two--dimension as well as on random complex networks; in the critical state fluctuations in an activity signal exhibit properties that are characteristic of avalanches observed in models of self-organized criticality, and these can be described by power--law distributions.

q-fin.GN↗
arXiv2013

Memoryless nonlinear response: A simple mechanism for the 1/f noise

Discovering the mechanism underlying the ubiquity of $"1/f^α"$ noise has been a long--standing problem. The wide range of systems in which the fluctuations show the implied long--time correlations suggests the existence of some simple and general mechanism that is independent of the details of any specific system. We argue here that a {\it memoryless nonlinear response} suffices to explain the observed non--trivial values of $α$: a random input noisy signal $S(t)$ with a power spectrum varying as $1/f^{α'}$, when fed to an element with such a response function $R$ gives an output $R(S(t))$ that can have a power spectrum $1/f^α$ with $α< α'$. As an illustrative example, we show that an input Brownian noise ($α'=2$) acting on a device with a sigmoidal response function $R(S)= \sgn(S)|S|^x$, with $x<1$, produces an output with $α= 3/2 +x$, for $0 \leq x \leq 1/2$. Our discussion is easily extended to more general types of input noise as well as more general response functions.

cond-mat.stat-mech↗
arXiv2012

Scaling behaviour in probabilistic neuronal cellular automata

We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective temperature). There are avalanches of neuronal activity, namely spatially and temporally contiguous sites of activity; a detailed numerical study of these activity avalanches is presented, and single, joint and marginal probability distributions are computed. At the critical point, we find that the scaling exponents for the variables are in good agreement with a mean--field theory.

cond-mat.stat-mech↗
arXiv2012

Power spectrum of mass and activity fluctuations in a sandpile

We consider a directed abelian sandpile on a strip of size $2\times n$, driven by adding a grain randomly at the left boundary after every $T$ time-steps. We establish the exact equivalence of the problem of mass fluctuations in the steady state and the number of zeroes in the ternary-base representation of the position of a random walker on a ring of size $3^n$. We find that while the fluctuations of mass have a power spectrum that varies as $1/f$ for frequencies in the range $ 3^{-2n} \ll f \ll 1/T$, the activity fluctuations in the same frequency range have a power spectrum that is linear in $f$.

cond-mat.stat-mech↗
arXiv2008

Strange nonchaotic attractors in driven delay--dynamics

Strange nonchaotic attractors (SNAs) are observed in quasiperiodically driven time--delay systems. Since the largest Lyapunov exponent is nonpositive, trajectories in two such identical but distinct systems show the property of {\it phase}--synchronization. Our results are illustrated in the model SQUID and Rössler oscillator systems.

nlin.CD↗
arXiv2004

Spectral Signatures of the Diffusional Anomaly in Water

Analysis of power spectrum profiles for various tagged particle quantities in bulk SPC/E water is used to demonstrate that variations in mobility associated with the diffusional anomaly are mirrored in the exponent of the \onebyf\ region. Monitoring of \onebyf behaviour is shown to be a simple and direct method for linking phenomena on three distinctive length and time scales: the local molecular environment, hydrogen bond network reorganisations and the diffusivity. The results indicate that experimental studies of supercooled water to probe the density dependence of $1/f^α$ spectral features, or equivalent stretched exponential behaviour in time-correlation functions, will be of interest.

cond-mat.soft↗
arXiv2002

Simplifying the mosaic description of DNA sequences

By using the Jensen-Shannon divergence, genomic DNA can be divided into compositionally distinct domains through a standard recursive segmentation procedure. Each domain, while significantly different from its neighbours, may however share compositional similarity with one or more distant (non--neighbouring) domains. We thus obtain a coarse--grained description of the given DNA string in terms of a smaller set of distinct domain labels. This yields a minimal domain description of a given DNA sequence, significantly reducing its organizational complexity. This procedure gives a new means of evaluating genomic complexity as one examines organisms ranging from bacteria to human. The mosaic organization of DNA sequences could have originated from the insertion of fragments of one genome (the parasite) inside another (the host), and we present numerical experiments that are suggestive of this scenario.

physics.bio-ph↗
arXiv2001

Dynamics of the Harper map: Localized states, Cantor spectra and Strange nonchaotic attractors

The Harper (or ``almost Mathieu'') equation plays an important role in studies of localization. Through a simple transformation, this equation can be converted into an iterative two dimensional skew--product mapping of the cylinder to itself. Localized states of the Harper system correspond to fractal attractors with nonpositive maximal Lyapunov exponent in the dynamics of the associated Harper map. We study this map and these strange nonchaotic attractors (SNAs) in detail in this paper. The spectral gaps of the Harper system have a unique labeling through a topological invariant of orbits of the Harper map. This labeling associates an integer index with each gap, and the scaling properties of the width of the gaps as a function of potential strength, $ε$ depends on the index. SNAs occur in a large region in parameter space: these regions have a tongue--like shape and end on a Cantor set on the line $ε= 1$ where the states are critically localized, and the spectrum is singular continuous. The SNAs of the Harper map are described in terms of their fractal properties, and the scaling behaviour of their power--spectra. These are created by unusual bifurcations and differ in many respects from SNAs that have hitherto been studied. The technique of studying a quantum eigenvalue problem in terms of the dynamics of an associated mapping can be applied to a number of related problems in 1~dimension. We discuss generalizations of the Harper potential as well as other quasiperiodic potentials in this context.

nlin.CD↗
arXiv2001

Strange Nonchaotic Attractors

Aperiodic dynamics which is nonchaotic is realized on Strange Nonchaotic attractors (SNAs). Such attractors are generic in quasiperiodically driven nonlinear systems, and like strange attractors, are geometrically fractal. The largest Lyapunov exponent is zero or negative: trajectories do not show exponential sensitivity to initial conditions. In recent years, SNAs have been seen in a number of diverse experimental situations ranging from quasiperiodically driven mechanical or electronic systems to plasma discharges. An important connection is the equivalence between a quasiperiodically driven system and the Schrödinger equation for a particle in a related quasiperiodic potential, giving a correspondence between the localized states of the quantum problem with SNAs in the related dynamical system. In this review we discuss the main conceptual issues in the study of SNAs, including the different bifurcations or routes for the creation of such attractors, the methods of characterization, and the nature of dynamical transitions in quasiperiodically forced systems. The variation of the Lyapunov exponent, and the qualitative and quantitative aspects of its local fluctuation properties, has emerged as an important means of studying fractal attractors, and this analysis finds useful application here. The ubiquity of such attractors, in conjunction with their several unusual properties, suggest novel applications.

nlin.CD↗
arXiv2001

Bifurcations and transitions in the quasiperiodically driven logistic map

We discuss several bifurcation phenomena that occur in the quasiperiodically driven logistic map. This system can have strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors; on SNAs the dynamics is aperiodic, but the largest Lyapunov exponent is nonpositive. There are a number of different transitions that occur here, from periodic attractors to SNAs, from SNAs to chaotic attractors, etc. We describe some of these transitions by examining the behavior of the largest Lyapunov exponent, distributions of finite time Lyapunov exponents and the invariant densities in the phase space.

nlin.CD↗
arXiv2001

A Plethora of Strange Nonchaotic Attractors

We show that it is possible to devise a large class of skew--product dynamical systems which have strange nonchaotic attractors (SNAs): the dynamics is asymptotically on fractal attractors and the largest Lyapunov exponent is nonpositive. Furthermore, we show that quasiperiodic forcing, which has been a hallmark of essentially allhitherto known examples of such dynamics is {\it not} necessary for the creation of SNAs.

nlin.CD↗
arXiv2001

Critical Localization and Strange Nonchaotic Dynamics: The Fibonacci Chain

The discrete Schrödinger equation with a quasiperiodic dichotomous potential specified by the Fibonacci sequence is known to have a singular continuous eigenvalue spectrum with all states being critically localized. This equation can be transformed into a quasiperiodic skew product dynamical system. In this iterative mapping which is entirely equivalent to the Schrödinger problem, critically localized states correspond to fractal attractors which have all Lyapunov exponents equal to zero. This provides an alternate means of studying the spectrum, as has been done earlier for the Harper equation. We study the spectrum of the Fibonacci system and describe the scaling of gap widths with potential strength.

nlin.CD↗
arXiv1999

Can Strange Nonchaotic Dynamics be induced through Stochastic Driving?

Upon addition of noise, chaotic motion in low-dimensional dynamical systems can sometimes be transformed into nonchaotic dynamics: namely, the largest Lyapunov exponent can be made nonpositive. We study this phenomenon in model systems with a view to understanding the circumstances when such behaviour is possible. This technique for inducing ``order'' through stochastic driving works by modifying the invariant measure on the attractor: by appropriately increasing measure on those portions of the attractor where the dynamics is contracting, the overall dynamics can be made nonchaotic, however {\it not} a strange nonchaotic attractor. Alternately, by decreasing measure on contracting regions, the largest Lyapunov exponent can be enhanced. A number of different chaos control and anticontrol techniques are known to function on this paradigm.

chao-dyn↗
arXiv1999

Collision and symmetry-breaking in the transition to strange nonchaotic attractors

Strange nonchaotic attractors (SNAs) can be created due to the collision of an invariant curve with itself. This novel ``homoclinic'' transition to SNAs occurs in quasiperiodically driven maps which derive from the discrete Schrödinger equation for a particle in a quasiperiodic potential. In the classical dynamics, there is a transition from torus attractors to SNAs, which, in the quantum system is manifest as the localization transition. This equivalence provides new insights into a variety of properties of SNAs, including its fractal measure. Further, there is a {\it symmetry breaking} associated with the creation of SNAs which rigorously shows that the Lyapunov exponent is nonpositive. By considering other related driven iterative mappings, we show that these characteristics associated with the the appearance of SNA are robust and occur in a large class of systems.

chao-dyn↗