We study excitation and suppression of chimera states in an ensemble of nonlocally coupled oscillators arranged in a framework of multiplex network. We consider the homogeneous network (all identical oscillators) with different parametric... more
We study excitation and suppression of chimera states in an ensemble of nonlocally coupled oscillators arranged in a framework of multiplex network. We consider the homogeneous network (all identical oscillators) with different parametric cases and interlayer heterogeneity by introducing parameter mismatch between the layers. We show the feasibility to suppress chimera states in the multiplex network via moderate interlayer interaction between a layer exhibiting chimera state and other layers which are in a coherent or incoherent state. On the contrary, for larger interlayer coupling, we observe the emergence of identical chimera states in both layers which we call an interlayer chimera state. We map the spatiotemporal behavior in a wide range of parameters, varying interlayer coupling strength and phase lag in two and three multiplexing layers. We also prove the emergence of interlayer chimera states in a multiplex network via evaluation of a continuous model. Furthermore, we consi...
A large parameter mismatch can induce amplitude death in two instantaneously coupled oscillators. Alternatively, a time delay in the coupling can induce amplitude death in two identical oscillators. We unify the mechanism of quenching of... more
A large parameter mismatch can induce amplitude death in two instantaneously coupled oscillators. Alternatively, a time delay in the coupling can induce amplitude death in two identical oscillators. We unify the mechanism of quenching of oscillation in coupled oscillators, either by a large parameter mismatch or a delay coupling, by a common lag scenario that is, surprisingly, different from the conventional lag synchronization. We present numerical as well as experimental evidence of this unknown kind of lag scenario when the lag increases with coupling and at a critically large value at a critical coupling strength, amplitude death emerges in two largely mismatched oscillators. This is analogous to amplitude death in identical systems with increasingly large coupling delay. In support, we use examples of the Chua oscillator and the Bonhoeffer-van der Pol system. Furthermore, we confirm this lag scenario during the onset of amplitude death in identical Stuart-Landau system under various instantaneous coupling forms, repulsive, conjugate, and a type of nonlinear coupling.
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ABSTRACT An experiment on generation of homoclinic chaos using two unidirectionally coupled Chua’s oscillators is described here. Homoclinic chaos is obtained at the response oscillator for weak coupling limit in the range of phase... more
ABSTRACT An experiment on generation of homoclinic chaos using two unidirectionally coupled Chua’s oscillators is described here. Homoclinic chaos is obtained at the response oscillator for weak coupling limit in the range of phase synchronization. Stable homoclinic oscillation is obtained by forcing periodic pulses to the driver. Phase locking of homoclinic oscillation to forcing pulse has been observed with different locking ratios (m:n), when the frequency of the pulse is close to time period of the homoclinic oscillation. © 2003 American Institute of Physics
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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... more
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 pseudorandom binary sequences with arbitrarily long recurrence times. As a consequence the attractors are geometrically fractal and the motion is aperiodic on experimentally accessible time scales. A practical realization of such attractors is demonstrated in an experiment using electronic circuits.
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Research Interests: Treatment, Macrophages, Cytotoxicity, Dendritic Cells, Biological Sciences, and 18 moreInfection and immunity, Spleen, Cell line, Humans, Liver, Infectious Disease, Mice, Animals, Infection, Visceral Leishmaniasis, Dendritic cell, Vaccination, Hybrid Solar Cells, Major histocompatibility complex, Interleukins, Protozoan Proteins, Membrane Protein, and Interleukin
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We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response.... more
We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response. The stability of the lag synchronization is ensured by using the Hurwitz matrix stability. We are able to scale up or down the size of a driver attractor at a response system in presence of a lag. This allows compensating the attenuation of the amplitude of a signal during transmission through a delay line. The delay coupling is illustrated with numerical examples of 3D systems, the Hindmarsh-Rose neuron model, the R\"ossler system and a Sprott system and, a 4D system. We implemented the coupling in electronic circuit to realize any desired lag synchronization in chaotic oscillators and scaling of attractors.
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Research Interests: Applied Mathematics, Algorithms, Nonlinear dynamics, Systems Theory, Ecology, and 17 moreCoupled Oscillator, Chaos, Numerical Simulation, Computer Simulation, Animals, Chaotic Dynamics, Time Delay, Nonlinear, Feedback, Phase Synchronization, Oscillations, Neurons, Lyapunov exponent, Nonlinear Dynamic System, Numerical Analysis and Computational Mathematics, Predatory Behavior, and Coupled Tank System
We report experimental observations of Shil'nikov-type homoclinic chaos and mixed-mode oscillations in asymmetry-induced Chua's oscillator. The asymmetry plays a crucial role in the related homoclinic bifurcation. The asymmetry is... more
We report experimental observations of Shil'nikov-type homoclinic chaos and mixed-mode oscillations in asymmetry-induced Chua's oscillator. The asymmetry plays a crucial role in the related homoclinic bifurcation. The asymmetry is introduced in the Chua circuit by forcing a dc voltage. Then by tuning a control parameter, we observed transition from large amplitude limit cycle to homoclinic chaos via a sequence of mixed-mode oscillations interspersed by chaotic states. We provide experimental evidences that the asymmetry effect can also be induced in the oscillatory Chua circuit when it is coupled with another one in a rest state. The coupling strength then controls the strength of asymmetry and thereby reproduces all the features of Shil'nikov chaos.
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We report for the first time the pattern dynamics in the vicinity of an inverse homoclinic bifurcation in an extended dissipative system. We observe, in direct numerical simulations of three dimensional Rayleigh-B\'{e}nard convection, a... more
We report for the first time the pattern dynamics in the vicinity of an inverse homoclinic bifurcation in an extended dissipative system. We observe, in direct numerical simulations of three dimensional Rayleigh-B\'{e}nard convection, a spontaneous breaking of a competition of two mutually perpendicular sets of oscillating cross rolls to one of two possible sets of oscillating cross rolls as the Rayleigh number is raised above a critical value. The time period of the cross-roll patterns diverges, and shows scaling behavior near the bifurcation point. This is an example of a transition from nonlocal to local pattern dynamics near an inverse homoclinic bifurcation. We also present a simple four-mode model that captures the pattern dynamics quite well.
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the... more
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.
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An experimental method of generating homoclinic: oscillation using two nonidentical Chua's oscillators coupled in unidirectional mode is described here. Homoclinic oscillation is obtained at the response oscillator in the... more
An experimental method of generating homoclinic: oscillation using two nonidentical Chua's oscillators coupled in unidirectional mode is described here. Homoclinic oscillation is obtained at the response oscillator in the weak coupling limit of phase synchronization. Different phase locking phenomena of homoclinic oscillation with external periodic pulse have been observed when the frequency of the pulse is close to the natural
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The phenomenon of emergent amplified response is reported in two unidirectionally coupled identical chaotic systems when heterogeneity as a parameter mismatch is introduced in a state of complete synchrony. The amplified response emerges... more
The phenomenon of emergent amplified response is reported in two unidirectionally coupled identical chaotic systems when heterogeneity as a parameter mismatch is introduced in a state of complete synchrony. The amplified response emerges from the interplay of heterogeneity and a type of cross-feedback coupling. It is reflected as an expansion of the response attractor in some directions in the state space of the coupled system. The synchronization manifold is simply rotated by the parameter detuning while its stability in the transverse direction is still maintained. The amplification factor is linearly related to the amount of parameter detuning. The phenomenon is elaborated with examples of the paradigmatic Lorenz system, the Shimizu-Morioka single-mode laser model, the Rössler system, and a Sprott system. Experimental evidence of the phenomenon is obtained in an electronic circuit. The method may provide an engineering tool for distortion-free amplification of chaotic signals.
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We report mixed lag synchronization in coupled counter-rotating oscillators. The trajectories of counter-rotating oscillators has opposite directions of rotation in uncoupled state. Under diffusive coupling via a scalar variable, a mixed... more
We report mixed lag synchronization in coupled counter-rotating oscillators. The trajectories of counter-rotating oscillators has opposite directions of rotation in uncoupled state. Under diffusive coupling via a scalar variable, a mixed lag synchronization emerges when a parameter mismatch is induced in two counter-rotating oscillators. In the state of mixed lag synchronization, one pair of state variables achieve synchronization shifted in time while another pair of state variables are in antisynchronization, however, they are too shifted by the same time. Numerical example of the paradigmatic R{\"o}ssler oscillator is presented and supported by electronic experiment.
... Kolkata, India Kolkata, India Potsdam, Germany Syamal Kumar Dana Prodyot Kumar Roy Jurgen Kurths Page 9. ... 229 T. Padma Subhadra, Tanusree Das and Nandini Chatterjee Singh The Role of Dynamical Instabilities and Fluctuations in... more
... Kolkata, India Kolkata, India Potsdam, Germany Syamal Kumar Dana Prodyot Kumar Roy Jurgen Kurths Page 9. ... 229 T. Padma Subhadra, Tanusree Das and Nandini Chatterjee Singh The Role of Dynamical Instabilities and Fluctuations in Hearing..... ...
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ABSTRACT Diagnosis of a single shunt fault in a ladder structure, by means of conventional input/output ports only and by making measurements at a single test frequency, is presented. Three sets of measurements, namely, forward... more
ABSTRACT Diagnosis of a single shunt fault in a ladder structure, by means of conventional input/output ports only and by making measurements at a single test frequency, is presented. Three sets of measurements, namely, forward attenuation, backward attenuation and a specific backward attenuation with an additional series arm impedance, with their corresponding phase-shifts for a sinusoidal input of a particular frequency, are found sufficient to diagnose a fault. The attenuations are expressed in terms of a set of polynomials defined by Morgan-Voyce (1959). The sum of forward and backward attenuation, as well as the difference between forward and the specific backward attenuation, in association with their corresponding phaseshifts, allow the authors to locate and identify faults. A proposition has been made to remove the ambiguities encountered in fault isolation towards the middle of the ladder structure
We report a general method of designing delay coupling for targeting a desired synchronization state in delay dynamical systems. We are able to target synchronization, antisynchronization, lag-, anti-lag synchronization, amplitude death... more
We report a general method of designing delay coupling for targeting a desired synchronization state in delay dynamical systems. We are able to target synchronization, antisynchronization, lag-, anti-lag synchronization, amplitude death and generalized synchronization in mismatched oscillators. We apply the theory for targeting a type of mixed synchronization where synchronization, antisynchronization and amplitude death coexist in different pairs of state
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We report an emergent bursting dynamics in a globally coupled network of mixed population of oscillatory and excitable Josephson junctions. The resistive-capacitive shunted junction (RCSJ) model of the superconducting device is considered... more
We report an emergent bursting dynamics in a globally coupled network of mixed population of oscillatory and
excitable Josephson junctions. The resistive-capacitive shunted junction (RCSJ) model of the superconducting
device is considered for this study. We focus on the parameter regime of the junction where its dynamics is
governed by the saddle-node on invariant circle (SNIC) bifurcation. For a coupling value above a threshold, the
network splits into two clusters when a reductionism approach is applied to reproduce the bursting behavior of
the large network. The excitable junctions effectively induce a slow dynamics on the oscillatory units to generate
parabolic bursting in a broad parameter space. We reproduce the bursting dynamics in a mixed population of
dynamical nodes of the Morris-Lecar model.
excitable Josephson junctions. The resistive-capacitive shunted junction (RCSJ) model of the superconducting
device is considered for this study. We focus on the parameter regime of the junction where its dynamics is
governed by the saddle-node on invariant circle (SNIC) bifurcation. For a coupling value above a threshold, the
network splits into two clusters when a reductionism approach is applied to reproduce the bursting behavior of
the large network. The excitable junctions effectively induce a slow dynamics on the oscillatory units to generate
parabolic bursting in a broad parameter space. We reproduce the bursting dynamics in a mixed population of
dynamical nodes of the Morris-Lecar model.
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The coexistence of infinitely many attractors is called extreme multistability in dynamical systems. In coupled systems, this phenomenon is closely related to partial synchrony and characterized by the emergence of a conserved quantity.... more
The coexistence of infinitely many attractors is called extreme multistability in dynamical systems. In coupled systems, this phenomenon is closely related to partial synchrony and characterized by the emergence of a conserved quantity. We propose a general design of coupling that leads to partial synchronization, which may be a partial complete synchronization or partial antisynchronization and even a mixed state of complete synchronization and antisynchronization in two coupled systems and, thereby reveal the emergence of extreme multistability. The proposed design of coupling has wider options and allows amplification or attenuation of the amplitude of the attractors whenever it is necessary. We demonstrate that this phenomenon is robust to parameter mismatch of the coupled oscillators.
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The effect of sinusoidal forcing on the RCLshunted junction is investigated here for the purpose of suppression of chaos. Numerical investigations show that the junction voltage of the superconductor is phase-locked (m:n) to sinusoidal... more
The effect of sinusoidal forcing on the RCLshunted junction is investigated here for the purpose of suppression of chaos. Numerical investigations show that the junction voltage of the superconductor is phase-locked (m:n) to sinusoidal forcing at forcing frequencies close to thenatural frequency of the junction. Control of chaos, in the sense of, converting chaos to periodicity is possible in this frequency range of the periodic forcing. Bifurcation route to chaos as period-doubling and torus breakdown have been observed near these forcing frequencies. Synchronization of two identical coupled junctions has also been reported.
In this Reply we answer the two major issues raised by the Comment. First, we point out that the idea of constructing extreme multistability in simple dynamical systems is not new and has been demonstrated previously by other authors.... more
In this Reply we answer the two major issues raised by the Comment. First, we point out that the idea of constructing extreme multistability in simple dynamical systems is not new and has been demonstrated previously by other authors. Furthermore, we emphasize the importance of the concept of a conserved quantity and its consequences for the dynamics, which applies to all the examples in the Comment. Second, we show that the design of controllers to achieve extreme multistability in coupled systems is as general as described in Phys. Rev. E 85, 035202(R) (2012) by providing two examples which do not lead to a master-slave dynamics.
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We report a design of coupling in chaotic oscillators for realizing a desired response: complete synchronization, antisynchronization and amplitude death simultaneously in different state variables of a system and thereby targeting a... more
We report a design of coupling in chaotic oscillators for realizing a desired response: complete synchronization, antisynchronization and amplitude death simultaneously in different state variables of a system and thereby targeting a control of synchronization. This is robust to parameter mismatch and the route of transition to synchrony obeys a scaling law. Experimental evidence of the coupling is presented using an electronic circuit.
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... Kolkata, India Kolkata, India Potsdam, Germany Syamal Kumar Dana Prodyot Kumar Roy Jurgen Kurths Page 9. ... 229 T. Padma Subhadra, Tanusree Das and Nandini Chatterjee Singh The Role of Dynamical Instabilities and Fluctuations in... more
... Kolkata, India Kolkata, India Potsdam, Germany Syamal Kumar Dana Prodyot Kumar Roy Jurgen Kurths Page 9. ... 229 T. Padma Subhadra, Tanusree Das and Nandini Chatterjee Singh The Role of Dynamical Instabilities and Fluctuations in Hearing..... ...
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... BRAJENDRA K. SINGH ∗ Department of Infectious Disease Epidemiology, Imperial College London, St Mary's Campus, London W2 1PG, UK b.singh@imperial.ac.uk SATYABRATA CHAKRABORTY and RAM CHANDRA YADAV ...