arXiv subjects

Ram Ramaswamy

Publications and source records attributed to Ram Ramaswamy.

16 recordsLinked to original sources

arXiv2026

Multi-cluster chimeras in phase oscillators with repulsive nonlocal coupling

Local repulsive coupling tend to a desynchronize ensembles of globally coupled oscillators, but when the repulsive coupling is nonlocal, multi-cluster chimeras can result. In this case, several groups of synchronized oscillators (the so-called clusters) are formed, and these coexist with a set of desynchronized oscillators. For phase oscillators on a ring with nonlocal piecewise linear repulsive coupling that also involves a phase lag, we find that in the multi-cluster chimera state the synchronized clusters are either antiphase or in splay with respect to each other, namely the n consecutive synchronized clusters differ in phase by 2π/n. This is in contrast to multi-cluster chimeras that are formed with nonlocal attractive coupling. The synchronized solutions are studied numerically as well as analytically and by analysing their stability, we identify the parameter regions where these can be observed. Our numerical results are validated by dimensional reduction using the Ott-Antonsen analysis.

nlin.AO↗

arXiv2026

The Directed Abelian Sandpile Model on Cylinders

We study the abelian sandpile model in two dimensions on a directed cylindrical lattice with periodic transverse boundary conditions in the transverse direction and dissipation at one boundary. Recurrent configurations form a finite abelian group, and repeated grain addition at a specific site generates deterministic dynamics on this group. Using Dhar's formulation, the sandpile group is identified with the co-kernel of the reduced directed Laplacian. We show that the group structure admits an exact reduction to a transverse problem, allowing complete determination of its cyclic decomposition. Our results establish a direct connection between the algebraic structure of the sandpile group and the periodicity of the driven dynamics, establishing the manner in which the underlying algebraic structure governs both deterministic and stochastic evolution in directed sandpile.

cond-mat.stat-mech↗

arXiv2025

Control Strategy for Generalized Synchrony in Coupled Dynamical Systems

Dynamical systems can be coupled in a manner that is designed to drive the resulting dynamics onto a specified lower dimensional submanifold in the phase space of the combined system. On the submanifold, the variables of the two systems have a well-specified functional relationship. This process can be viewed as a control technique that ensures generalized synchronization. Depending on the nature of the dynamical systems and the specified submanifold, different coupling functions can be derived in order to achieve a desired control objective. We discuss a circuit implementation of this strategy for coupled chaotic Lorenz oscillators, as well as a demonstration of the methodology for designing coordinated motion (swarming) in a set of autonomous drones.

nlin.CD↗

arXiv2025

Dynamics of coupled $D$-dimensional Stuart-Landau oscillators

The Stuart-Landau oscillator generalized to $D > 2$ dimensions has SO($D$) rotational symmetry. We study the collective dynamics of a system of $K$ such oscillators of dimensions $D =$ 3 and 4, with coupling chosen to either preserve or break rotational symmetry. This leads to emergent dynamical phenomena that do not have analogs in the well-studied case of $D=2$. Further, the larger number of internal parameters allows for the exploration of different forms of heterogeneity among the individual oscillators. When rotational symmetry is preserved there can be various forms of synchronization as well as multistability and $partial$ amplitude death, namely, the quenching of oscillations within a subset of variables that asymptote to the same constant value. The oscillatory dynamics in these cases are characterized by phase-locking and phase-drift. When the coupling breaks rotational symmetry we observe $partial$ synchronization (when a subset of the variables coincide and oscillate) and $partial$ oscillation death (when a subset of variables asymptote to different stationary values), as well as the coexistence of these different partial quenching phenomena.

nlin.CD↗

arXiv2025

Exactly solvable Stuart-Landau models in arbitrary dimensions

We use Clifford's geometric algebra to extend the Stuart-Landau system to dimensions $D >2$ and give an exact solution of the oscillator equations in the general case. At the supercritical Hopf bifurcation marked by a transition from stable fixed-point dynamics to oscillatory motion, the Jacobian matrix evaluated at the fixed point has $N=\lfloor{D/2}\rfloor$ pairs of complex conjugate eigenvalues which cross the imaginary axis simultaneously. For odd $D$ there is an additional purely real eigenvalue that does the same. Oscillatory dynamics is asymptotically confined to a hypersphere $\mathbb{S}^{D-1}$ and is characterised by extreme multistability, namely the coexistence of an infinite number of limiting orbits each of which has the geometry of a torus $\mathbb{T}^N$ on which the motion is either periodic or quasiperiodic. We also comment on similar Clifford extensions of other limit cycle oscillator systems and their generalisations.

nlin.CD↗

arXiv2022

Response to the COVID-19 Pandemic: Physics Teaching in India

When academic institutions in India closed abruptly in March 2020 due to the COVID-19 pandemic, formal education moved online. This transition had a very uneven impact given the significant digital divide between rural and urban India and the unequal distribution of digital resources in different institutions. Access to resources varied substantially by individual, based on socioeconomic factors as well as gender. Institutional support to the academic community during this critical period was largely inadequate, which has had serious consequences on the teaching of physics and other subjects that require laboratory instruction. Educational institutions also provide safe and enabling learning spaces for women students; reduced access to such facilities undermined the work- and study-related dynamics for women because of the scarcity of resources such as devices, data, and time. This paper reports on efforts made towards understanding such challenges during the COVID-19 pandemic and describes steps that were taken to address them.

physics.ed-ph↗

arXiv2015

Synchronization efficiency in coupled stochastic oscillators: The role of connection topology

We study the efficiency of synchronization in ensembles of identical coupled stochastic oscillator systems. By deriving a chemical Langevin equation, we measure the rate at which the systems synchronize. The rate at which the difference in the Hilbert phases of the systems evolve provides a suitable order parameter, and a 2--dimensional recurrence plot further facilitates the analysis of stochastic synchrony. We find that a global mean--field coupling effects the most rapid approach to global synchrony, and that when the number of "information carrying" molecular species increases, the rate of synchrony increases. The Langevin analysis is complemented by numerical simulations.

q-bio.SC↗

arXiv2014

Dynamics of stress p53: Nitric oxide induced transition of states and synchronization

We study the temporal and the synchronous behaviours in p53-Mdm2 regulatory network due to the interaction of its complex network components with the nitric oxide molecule. In single cell process, increase in nitric oxide concentration gives rise the transition to various p53 temporal behaviours, namely fixed point oscillation, damped oscillation and sustain oscillation indicating stability, weakly activated and strongly activated states. The noise in stochastic system is found to help to reach these states much faster as compared to deterministic case which is evident from permutation entropy dynamics. In coupled system with nitric oxide as diffusively coupling molecule, we found nitric oxide as strong coupling molecule within a certain range of coupling strength εbeyond which it become weak synchronizing agent. We study these effects by using correlation like synchronization indicator γobtained from permutation entropies of the coupled system, and found five important regimes in (ε-γ) phase diagram, indicating desynchronized, transition, strongly synchronized, moderately synchronized and weakly synchronized regimes respectively. We claim that there is the competition between the toxicity and the synchronizing role of nitric oxide that lead the cell in different stressed conditions.

q-bio.MN↗

arXiv2013

Amplitude Death: The cessation of oscillations in coupled nonlinear dynamical systems

Here we extend a recent review (Physics Reports {\bf 521}, 205 (2012)) of amplitude death, namely the suppression of oscillations due to the coupling interactions between nonlinear dynamical systems. This is an important emergent phenomenon that is operative under a variety of scenarios. We summarize results of recent studies that have significantly added to our understanding of the mechanisms that underlie the process, and also discuss the phase--flip transition, a characteristic and unusual effect that occurs in the transient dynamics as the oscillations die out.

nlin.CD↗

arXiv2013

Amplitude death phenomena in delay--coupled Hamiltonian systems

Hamiltonian systems, when coupled {\it via} time--delayed interactions, do not remain conservative. In the uncoupled system, the motion can typically be periodic, quasiperiodic or chaotic. This changes drastically when delay coupling is introduced since now attractors can be created in the phase space. In particular for sufficiently strong coupling there can be amplitude death (AD), namely the stabilization of point attractors and the cessation of oscillatory motion. The approach to the state of AD or oscillation death is also accompanied by a phase--flip in the transient dynamics. A discussion and analysis of the phenomenology is made through an application to the specific cases of harmonic as well as anharmoniccoupled oscillators, in particular the Hénon-Heiles system.

nlin.CD↗

arXiv2013

Driving--induced bistability in coupled chaotic attractors

We examine the effects of symmetry--preserving and breaking interactions in a drive--response system where the response has an invariant symmetry in the absence of the drive. Subsequent to the onset of generalized synchronization, we find that there can be more than one stable attractor. Numerical, as well as analytical results establish the presence of phase synchrony in such coexisting attractors. These results are robust to external noise.

nlin.CD↗

arXiv2012

Amplitude Death: The emergence of stationarity in coupled nonlinear systems

When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

nlin.CD↗

arXiv2011

Relaying phase synchrony in chaotic oscillator chains

We study the manner in which the effect of an external drive is transmitted through mutually coupled response systems by examining the phase synchrony between the drive and the response. Two different coupling schemes are used. Homogeneous couplings are via the same variables, while heterogeneous couplings are through different variables. With the latter scenario, synchronization regimes are truncated with increasing number of mutually coupled oscillators, in contrast to homogeneous coupling schemes. Our results are illustrated for systems of coupled chaotic Rössler oscillators.

nlin.CD↗

arXiv2009

Design strategies for the creation of aperiodic nonchaotic attractors

Parametric modulation in nonlinear dynamical systems can give rise to attractors on which the dynamics is aperiodic and nonchaotic, namely with largest Lyapunov exponent being nonpositive. We describe a procedure for creating such attractors by using random modulation or pseudo-random binary sequences with arbitrarily long recurrence times. As a consequence the attractors are geometrically fractal and the motion is aperiodic on experimentally accessible timescales. A practical realization of such attractors is demonstrated in an experiment using electronic circuits.

nlin.CD↗

arXiv2006

The synchronization of stochastic oscillators

We examine microscopic mechanisms for coupling stochastic oscillators so that they display similar and correlated temporal variations. Unlike oscillatory motion in deterministic dynamical systems, complete synchronization of stochastic oscillators does not occur, but appropriately defined oscillator phase variables coincide. This is illustrated in model chemical systems and genetic networks that produce oscillations in the dynamical variables, and we show that suitable coupling of different networks can result in their phase synchronization.

q-bio.QM↗

arXiv2002

Global Optimization by Adiabatic Switching

We apply a recently introduced method for global optimization to determine the ground state energy and configuration for model metallic clusters. The global minimum for a given N-atom cluster is found by following the damped dynamics of the N particle system on an evolving potential energy surface. In this application, the time dependent interatomic potential interpolates adiabatically between the Lennard-Jones (LJ) and the Sutton-Chen (SC) forms. Starting with an ensemble of initial conditions corresponding to the ground state configuration of the Lennard-Jones cluster, the system asymptotically reaches the ground state of the Sutton-Chen cluster. We describe the method and present results for specific cluster size N=15, when the ground state symmetry of LJ$_N$ and SC$_N$ differ.

physics.comp-ph↗