Publications

@article{PhysRevE.98.032217,
title = {Design strategies for generalized synchronization},
author = {S Chishti and R Ramaswamy },
url = {https://link.aps.org/doi/10.1103/PhysRevE.98.032217},
doi = {10.1103/PhysRevE.98.032217},
issn = {2470-0053 },
year = {2018},
date = {2018-09-24},
journal = {Physical Review E},
volume = {98},
pages = {032217},
abstract = {We describe a general procedure to couple two dynamical systems so as to guide their joint dynamics onto a specific transversally stable invariant submanifold in the phase space. This method can thus be viewed as a means of constraining the dynamics, with the coupling functions providing the forces of constraint, which results in the coupled systems being in generalized synchronization. The required coupling functions are, however, not uniquely defined and can therefore be chosen in order to satisfy a desired design criterion.},
keywords = {Generalized Synchronization, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Ujjwal2016,
title = {Phase oscillators in modular networks: The effect of nonlocal coupling},
author = {Sangeeta Rani Ujjwal and Nirmal Punetha and Ramakrishna Ramaswamy},
url = {https://ramramaswamy.org/papers/161.pdf},
doi = {10.1103/PhysRevE.93.012207},
issn = {24700053},
year = {2016},
date = {2016-01-01},
journal = {Physical Review E},
volume = {93},
number = {1},
pages = {1–10},
abstract = {We study the dynamics of nonlocally coupled phase oscillators in a modular network. The interactions include a phase lag, $alpha$. Depending on the various parameters the system exhibits a number of different dynamical states. In addition to global synchrony there can also be modular synchrony when each module can synchronize separately to a different frequency. There can also be multicluster frequency chimeras, namely coherent domains consisting of modules that are separately synchronized to different frequencies, coexisting with modules within which the dynamics is desynchronized. We apply the Ott-Antonsen ansatz in order to reduce the effective dimensionality and thereby carry out a detailed analysis of the different dynamical states.},
keywords = {Modular Network, Nonlocal Coupling, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Kumar2016,
title = {Synchronization properties of coupled chaotic neurons: The role of random shared input},
author = {Rupesh Kumar and Shakir Bilal and Ram Ramaswamy},
url = {http://dx.doi.org/10.1063/1.4954377},
doi = {10.1063/1.4954377},
issn = {10541500},
year = {2016},
date = {2016-01-01},
journal = {Chaos},
volume = {26},
number = {6},
abstract = {textcopyright 2016 Author(s). Spike-time correlations of neighbouring neurons depend on their intrinsic firing properties as well as on the inputs they share. Studies have shown that periodically firing neurons, when subjected to random shared input, exhibit asynchronicity. Here, we study the effect of random shared input on the synchronization of weakly coupled chaotic neurons. The cases of so-called electrical and chemical coupling are both considered, and we observe a wide range of synchronization behaviour. When subjected to identical shared random input, there is a decrease in the threshold coupling strength needed for chaotic neurons to synchronize in-phase. The system also supports lag-synchronous states, and for these, we find that shared input can cause desynchronization. We carry out a master stability function analysis for a network of such neurons and show agreement with the numerical simulations. The contrasting role of shared random input for complete and lag synchronized neurons is useful in understanding spike-time correlations observed in many areas of the brain.},
keywords = {Neurons, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Punetha2015,
title = {Delay-induced remote synchronization in bipartite networks of phase oscillators},
author = {Nirmal Punetha and Sangeeta Rani Ujjwal and Fatihcan M Atay and Ramakrishna Ramaswamy},
url = {https://ramramaswamy.org/papers/159.pdf},
doi = {10.1103/PhysRevE.91.022922},
issn = {15502376},
year = {2015},
date = {2015-01-01},
journal = {Physical Review E – Statistical, Nonlinear, and Soft Matter Physics},
volume = {91},
number = {2},
pages = {1–7},
abstract = {We study a system of mismatched oscillators on a bipartite topology with time-delay coupling, and analyze the synchronized states. For a range of parameters, when all oscillators lock to a common frequency, we find solutions such that systems within a partition are in complete synchrony, while there is lag synchronization between the partitions. Outside this range, such a solution does not exist and instead one observes scenarios of remote synchronization—namely, chimeras and individual synchronization, where either one or both of the partitions are synchronized independently. In the absence of time delay such states are not observed in phase oscillators.},
keywords = {Bipartite Network, Delay, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Punetha2015a,
title = {Bipartite networks of oscillators with distributed delays: Synchronization branches and multistability},
author = {Nirmal Punetha and Ramakrishna Ramaswamy and Fatihcan M Atay},
url = {https://ramramaswamy.org/papers/160.pdf},
doi = {10.1103/PhysRevE.91.042906},
issn = {15502376},
year = {2015},
date = {2015-01-01},
journal = {Physical Review E – Statistical, Nonlinear, and Soft Matter Physics},
volume = {91},
number = {4},
pages = {1–10},
abstract = {We study synchronization in bipartite networks of phase oscillators with general nonlinear coupling and distributed time delays. Phase-locked solutions are shown to arise, where the oscillators in each partition are perfectly synchronized among themselves but can have a phase difference with the other partition, with the phase difference necessarily being either zero or $pi$ radians. Analytical conditions for the stability of both types of solutions are obtained and solution branches are explicitly calculated, revealing that the network can have several coexisting stable solutions. With increasing value of the mean delay, the system exhibits hysteresis, phase flips, final state sensitivity, and an extreme form of multistability where the numbers of stable in-phase and antiphase synchronous solutions with distinct frequencies grow without bound. The theory is applied to networks of Landau-Stuart and Rossler oscillators and shown to accurately predict both in-phase and antiphase synchronous behavior in appropriate parameter ranges.},
keywords = {Bipartite Network, Multistability, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Saxena2014,
title = {Amplitude death: The cessation of oscillations in coupled nonlinear dynamical systems},
author = {Garima Saxena and Nirmal Punetha and Awadhesh Prasad and Ram Ramaswamy},
url = {https://ramramaswamy.org/papers/RC44.pdf},
doi = {10.1063/1.4865354},
issn = {15517616},
year = {2014},
date = {2014-01-01},
journal = {AIP Conference Proceedings},
volume = {1582},
pages = {158–171},
abstract = {Here we extend a recent review (Physics Reports $backslash$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.},
keywords = {Amplitude quenching, Bifurcation, Control Network, Fixed-point solution, Interaction, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Alam2012,
title = {Stochastic synchronization of interacting pathways in testosterone model},
author = {Md Jahoor Alam and Gurumayum Reenaroy Devi and K.Brojen R Singh and R Ramaswamy and Sonu Chand Thakur and Indrajit B Sharma},
url = {http://dx.doi.org/10.1016/j.compbiolchem.2012.08.001},
doi = {10.1016/j.compbiolchem.2012.08.001},
issn = {14769271},
year = {2012},
date = {2012-01-01},
journal = {Computational Biology and Chemistry},
volume = {41},
pages = {10–17},
publisher = {Elsevier Ltd},
abstract = {We examine the possibilities of various coupling mechanisms among a group of identical stochastic oscillators via Chemical Langevin formalism where each oscillator is modeled by stochastic model of testosterone (T) releasing pathway. Our results show that the rate of synchrony among the coupled oscillators depends on various parameters namely fluctuating factor, coupling constants $epsilon$, and interestingly on system size. The results show that synchronization is achieved much faster in classical deterministic system rather than stochastic system. Then we do large scale simulation of such coupled pathways using stochastic simulation algorithm and the detection of synchrony is measured by various order parameters such as synchronization manifolds, phase plots etc and found that the proper synchrony of the oscillators is maintained in different coupling mechanisms and support our theoretical claims. We also found that the coupling constant follows power law behavior with the systems size (V) by $epsilon$ ∼ AV-$gamma$, where $gamma$ = 1 and A is a constant. We also examine the phase transition like behavior in all coupling mechanisms that we have considered for simulation. The behavior of the system is also investigated at thermodynamic limit; where V→ ∞, molecular population, N→ ∞ but NV→finite, to see the role of noise in information processing and found the destructive role in the rate of synchronization. textcopyright 2012 Elsevier Ltd. All rights reserved.},
keywords = {Cell signaling, Coupling, Intercellular communication, Intracellular communication, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Saxena2012,
title = {Amplitude death: The emergence of stationarity in coupled nonlinear systems},
author = {Garima Saxena and Awadhesh Prasad and Ram Ramaswamy},
url = {https://ramramaswamy.org/papers/RC43.pdf},
doi = {10.1016/j.physrep.2012.09.003},
issn = {03701573},
year = {2012},
date = {2012-01-01},
journal = {Physics Reports},
volume = {521},
number = {5},
pages = {205–228},
abstract = {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 which the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behavior 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. textcopyright 2012 Elsevier B.V.},
keywords = {Amplitude quenching, Bifurcation, Control, Fixed-point solution, Interaction, Network, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Saxena2011,
title = {The effect of finite response-time in coupled dynamical systems},
author = {Garima Saxena and Awadhesh Prasad and Ram Ramaswamy},
url = {https://ramramaswamy.org/papers/RC41.pdf},
doi = {10.1007/s12043-011-0179-z},
issn = {03044289},
year = {2011},
date = {2011-01-01},
journal = {Pramana – Journal of Physics},
volume = {77},
number = {5},
pages = {865–871},
abstract = {The paper investigates synchronization in unidirectionally coupled dynamical systems wherein the influence of drive on response is cumulative: coupling signals are integrated over a time interval t . A major consequence of integrative coupling is that the onset of the generalized and phase synchronization occurs at higher coupling compared to the instantaneous (t = 0) case. The critical coupling strength at which synchronization sets in is found to increase with t . The systems explored are the chaotic Rössler and limit cycle (the Landau-Stuart model) oscillators. For coupled Rössler oscillators the region of generalized synchrony in the phase space is intercepted by an asynchronous region which corresponds to anomalous generalized synchronization. textcopyright Indian Academy of Sciences.},
keywords = {Distributed delay, Drive-response, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Agrawal2010,
title = { Quasiperiodic forcing of coupled chaotic systems},
author = {M Agrawal, A Prasad, and R Ramaswamy},
url = {https://link.aps.org/doi/10.1103/PhysRevE.81.026202},
doi = {10.1103/PhysRevE.81.026202},
year = {2010},
date = {2010-02-04},
journal = {Physical Review E},
volume = {81},
number = {2},
pages = {026202},
abstract = {We study the manner in which the effect of quasiperiodic modulation is transmitted in a coupled nonlinear dynamical system. A system of Rössler oscillators is considered, one of which is subject to driving, and the dynamics of other oscillators which are, in effect, indirectly forced is observed. Strange nonchaotic dynamics is known to arise only in quasiperiodically driven systems, and thus the transmitted effect is apparent when such motion is seen in subsystems that are not directly modulated. We also find instances of imperfect phase synchronization with forcing, where the system transits from one phase synchronized state to another, with arbitrary phase slips. The stability of phase synchrony for arbitrary initial conditions with identical forcing is observed as a general property of strange nonchaotic motion.},
keywords = {Quasiperiodicity, Strange nonchaotic attractors, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Shrimali2010,
title = {Delay-coupled discrete maps: Synchronization, bistability, and quasiperiodicity},
author = {Manish Dev Shrimali and Rangoli Sharan and Awadhesh Prasad and Ram Ramaswamy},
url = {https://ramramaswamy.org/papers/129.pdf},
doi = {10.1016/j.physleta.2010.04.048},
issn = {03759601},
year = {2010},
date = {2010-01-01},
journal = {Physics Letters, Section A: General, Atomic and Solid State Physics},
volume = {374},
number = {26},
pages = {2636–2639},
abstract = {The synchronization transition is studied in delay-coupled logistic maps. For low coupling, in-phase and out-of-phase synchronous dynamics coexist, and with increasing coupling there is a regime of quasiperiodicity before eventual attraction to a fixed point at a critical value of coupling that depends on the nonlinearity. The presence of a region of asynchrony separating two synchronized regimes-termed anomalous behaviour-has been observed earlier in continuous systems and is shown here to occur in delay mappings as well. There are regions of in-phase, anti-phase, and out-of-phase dynamics of periodic as well as chaotic attractors. textcopyright 2010 Elsevier B.V.},
keywords = {Coupled maps, Delay coupling, Synchronization},
pubstate = {published},
tppubtype = {article}
}

@article{Prasad2008b,
title = {The effect of time–delay on anomalous phase synchronization},
author = {A Prasad, J Kurths and R Ramaswamy},
url = {https://doi.org/10.1016/j.physleta.2008.08.043},
doi = {10.1016/j.physleta.2008.08.043},
year = {2008},
date = {2008-09-29},
journal = {Physics Letters A},
volume = {372},
number = {40},
pages = {6150-6154},
abstract = {Anomalous phase synchronization in nonidentical interacting oscillators is manifest as the increase of frequency disorder prior to synchronization. We show that this effect can be enhanced when a time-delay is included in the coupling. In systems of limit-cycle and chaotic oscillators we find that the regions of phase disorder and phase synchronization can be interwoven in the parameter space such that as a function of coupling or time-delay the system shows transitions from phase ordering to disorder and back.},
keywords = {Synchronization, Time Delay},
pubstate = {published},
tppubtype = {article}
}