arXiv subjects

V. K. Chandrasekar

Publications and source records attributed to V. K. Chandrasekar.

At least 73 records · Page 4Linked to original sources

arXiv2019

Affinity-based measurement-induced nonlocality and its robustness against noise

Measurement-induced nonlocality (MIN), a quantum correlation measure for the bipartite system, is an indicator of global effects due to locally invariant von Neumann projective measurements. It is well known fact that the correlation measures based on Hilbert-Schmidt norm are not credible measure in capturing nonlocal attributes of a quantum state. In this article, to remedy the local ancilla problem of Hilbert-Schmidt norm based MIN, we propose a new form of MIN-based on affinity. This quantity satisfies all criteria of a bonafide measure of quantum correlation measure. For an arbitrary pure state, it is shown that affinity based MIN equals to other forms of geometric versions of correlation measure. We obtain an upper bound of this measure for m \times n-dimensional arbitrary mixed state. We obtain a closed formula of the proposed version of MIN for 2 \times n dimensional (qubit qudit) mixed state. We apply these results on two-qubit mixed states such as Werner, isotropic and Bell diagonal state. To illustrate the robustness of affinity-based measure against noise, we study the dynamics of MIN under generalized amplitude damping channel.

quant-ph↗

arXiv2019

Phase locking of spin transfer nano-oscillators using common microwave sources

In this paper, we study typical nonlinear phenomenon of phase-locking or synchronization in spin-torque nano oscillators (STNOs). To start with the oscillators are considered as uncoupled but interlinked through either a common microwave current or a microwave field. We identify the phase locking of an array of STNOs (first for two and then for 100 oscillators) by means of injection locking which represents locking the oscillations to a common alternating spin current or a common microwave magnetic field. We characterize the locking of STNOs through both first and second harmonic lockings in an array. We find that second harmonic lockings takes lesser value of microwave current and field when compared with the first harmonic lockings. Our results also show that oscillating microwave current can induce integer harmonic locking while microwave field can induce both integer and several fractional harmonic lockings. We also extend our analysis to study locking behavior of two STNOs by introducing time delay feedback and coupling through a current injection and bring out the associated locking characteristics. Finally, we have also analyzed the stability of synchronization of identical array of STNOs with current coupling by using master stability function formalism.

cond-mat.mes-hall↗

arXiv2019

Long-range interaction induced collective dynamical behaviors

Long-range interacting systems are omnipresent in nature. We investigate here the collective dynamical behavior in a long-range interacting system consisting of coupled Stuart-Landau limit cycle oscillators. In particular, we analyze the impact of a repulsive coupling along with symmetry breaking coupling. We report that the addition of repulsive coupling of sufficient strength can induce a swing of the synchronized state which will start disappearing with an increasing disorder as a function of the repulsive coupling. We also deduce analytical stability conditions for the oscillatory states including synchronized state, solitary state, two-cluster state as well as oscillation death state. Finally, we have also analyzed the effect of power-law exponent on the observed dynamical states.

nlin.AO↗

arXiv2019

Frustration induced transient chaos, fractal and riddled basins in coupled limit cycle oscillators

This report unravels frustration as a source of transient chaotic dynamics even in a simple array of coupled limit cycle oscillators. The transient chaotic dynamics along with the multistable nature of frustrated systems facilitates the existence of complex basin structures such as fractal and riddled basins. In particular, we report the emergence of transient chaotic dynamics around the chaotic itinerancy region, where the basin of attraction near the chaotic region is riddled and it becomes fractal basin when we move away from this region. Normally the complex basin structures are observed only for oscillatory states but surprisingly it is also observed even for oscillation death states. Interestingly super persistent transient chaos is also shown to emerge in the coupled limit cycle oscillators, which manifests as stable chaos for larger networks.

nlin.AO↗

arXiv2018

Conjugate coupling induced symmetry breaking and quenched oscillations

Spontaneous symmetry breaking (SSB) is essential and plays a vital role many natural phenomena, including the formation of Turing pattern in organisms and complex patterns in brain dynamics. In this work, we investigate whether a set of coupled Stuart-Landau oscillators can exhibit spontaneous symmetry breaking when the oscillators are interacting through dissimilar variables or conjugate coupling. We find the emergence of SSB state with coexisting distinct dynamical states in the parametric space and show how the system transits from symmetry breaking state to out-of-phase synchronized (OPS) state while admitting multistabilities among the dynamical states. Further, we also investigate the effect of feedback factor on SSB as well as oscillation quenching states and we point out that the decreasing feedback factor completely suppresses SSB and oscillation death states. Interestingly, we also find the feedback factor completely diminishes only symmetry breaking oscillation and oscillation death (OD) states but it does not affect the nontrivial amplitude death (NAD) state. Finally, we have deduced the analytical stability conditions for in-phase and out-of-phase oscillations, as well as amplitude and oscillation death states.

nlin.AO↗

arXiv2018

Distinct collective states due to the trade-off between attractive and repulsive couplings

We investigate the effect of repulsive coupling together with an attractive coupling in a network of nonlocally coupled oscillators. To understand the complex interaction between these two couplings we introduce a control parameter in the repulsive coupling which plays a crucial role in inducing distinct complex collective patterns. In particular, we show the emergence of various cluster chimera death states through a dynamically distinct transition route, namely the oscillatory cluster state and coherent oscillation death state as a function of the repulsive coupling in the presence of the attractive coupling. In the oscillatory cluster state, the oscillators in the network are grouped into two distinct dynamical states of homogeneous and inhomogeneous oscillatory states. Further, the network of coupled oscillators follows the same transition route in the entire coupling range. Depending upon distinct coupling ranges the system displays a different number of clusters in the death state and oscillatory state. We also observe that the number of coherent domains in the oscillatory cluster state exponentially decreases with increase in coupling range and obeys a power law decay. Additionally, we show analytical stability for observed solitary state, synchronized state, and incoherent oscillation death state.

nlin.AO↗

arXiv2018

Stable amplitude chimera states in a network of locally coupled Stuart-Landau oscillators

We investigate the occurrence of collective dynamical states such as transient amplitude chimera, stable amplitude chimera and imperfect breathing chimera states in a \textit{locally coupled} network of Stuart-Landau oscillators. In an imperfect breathing chimera state, the synchronized group of oscillators exhibits oscillations with large amplitudes while the desynchronized group of oscillators oscillates with small amplitudes and this behavior of coexistence of synchronized and desynchronized oscillations fluctuates with time. Then we analyze the stability of the amplitude chimera states under various circumstances, including variations in system parameters and coupling strength, and perturbations in the initial states of the oscillators. For an increase in the value of the system parameter, namely the nonisochronicity parameter, the transient chimera state becomes a stable chimera state for a sufficiently large value of coupling strength. In addition, we also analyze the stability of these states by perturbing the initial states of the oscillators. We find that while a small perturbation allows one to perturb a large number of oscillators resulting in a stable amplitude chimera state, a large perturbation allows one to perturb a small number of oscillators to get a stable amplitude chimera state. We also find the stability of the transient and stable amplitude chimera states as well as traveling wave states for appropriate number of oscillators using Floquet theory. In addition, we also find the stability of the incoherent oscillation death states.

nlin.AO↗

arXiv2017

Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

A complex collective emerging behavior characterized by coexisting coherent and incoherent do- mains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators driven by a common dynamic environment. The latter facilitates the onset of phase-flip bifurcation/transitions among the coupled oscillators of the ensemble, while the nonlocal coupling induces a partial asynchronization among the out-of-phase synchronized oscillators at this onset. This leads to the manifestation of coexisting out-of-phase synchronized coherent domains interspersed by asynchronous incoherent domains elucidating the existence of a different type of chimera state. In addition to this, a rich variety of other collective behaviors such as clusters with phase-flip transition, conventional chimera, solitary state and com- plete synchronized state which have been reported using different coupling architectures are found to be induced by the employed couplings for appropriate coupling strengths. The robustness of the resulting dynamics is demonstrated in ensembles of two paradigmatic models, namely Rössler oscillators and Stuart-Landau oscillators.

nlin.CD↗

arXiv2017

A note on deriving linearizing transformations for a class of second order nonlinear ordinary differential equations

We present a method of deriving linearizing transformations for a class of second order nonlinear ordinary differential equations. We construct a general form of a nonlinear ordinary differential equation that admits Bernoulli equation as its first integral. We extract conditions for this integral to yield three different linearizing transformations, namely point, Sundman and generalized linearizing transformations. The explicit forms of these linearizing transformations are given. The exact forms and the general solution of the nonlinear ODE for these three linearizables cases are also enumerated. We illustrate the procedure with three different examples.

nlin.SI↗

arXiv2017

Spontaneous symmetry breaking due to the trade-off between attractive and repulsive couplings

Spontaneous symmetry breaking (SSB) is an important phenomenon observed in various fields including physics and biology. In this connection, we here show that the trade-off between attractive and repulsive couplings can induce spontaneous symmetry breaking in a homogeneous system of coupled oscillators. With a simple model of a system of two coupled Stuart-Landau oscillators, we demonstrate how the tendency of attractive coupling in inducing in-phase synchronized (IPS) oscillations and the tendency of repulsive coupling in inducing out-of-phase synchronized (OPS) oscillations compete with each other and give rise to symmetry breaking oscillatory (SBO) states and interesting multistabilities. Further, we provide explicit expressions for synchronized and anti-synchronized oscillatory states as well as the so called oscillation death (OD) state and study their stability. If the Hopf bifurcation parameter ($λ$) is greater than the natural frequency ($ω$) of the system, the attractive coupling favours the emergence of an anti-symmetric OD state via a Hopf bifurcation whereas the repulsive coupling favours the emergence of a similar state through a saddle-node bifurcation. We show that an increase in the repulsive coupling not only destabilizes the IPS state but also facilitates the re-entrance of the IPS state.

nlin.AO↗

arXiv2017

Controlling of blow-up responses by a nonlinear $\cal{PT}$ symmetric coupling

We investigate the dynamics of a coupled waveguide system with competing linear and nonlinear loss-gain profiles which can facilitate power saturation. We show the usefulness of the model in achieving unidirectional beam propagation. In this regard, the considered type of coupled waveguide system has two drawbacks, (i) difficulty in achieving perfect isolation of light in a waveguide and (ii) existence of blow-up type behavior for certain input power situations. We here show a nonlinear $\cal{PT}$ symmetric coupling that helps to overcome these two drawbacks. Such a nonlinear coupling has close connection with the phenomenon of stimulated Raman scattering. In particular, we have elucidated the role of this nonlinear coupling using an integrable $\cal{PT}$ symmetric situation. In particular, using the integrals of motion, we have reduced this coupled waveguide problem to the problem of dynamics of a particle in a potential. With the latter picture, we have clearly illustrated the role of the considered nonlinear coupling. The above $\cal{PT}$ symmetric case corresponds to a limiting form of a general equation describing the phenomenon of stimulated Raman scattering. We also point out the ability to transport light unidirectionally even in this general case.

nlin.PS↗

arXiv2017

Chimera-like states in two distinct groups of identical populations of coupled Stuart-Landau oscillators

We show the existence of chimera-like states in two distinct groups of identical populations of globally coupled Stuart-Landau oscillators. The existence of chimera-like states occurs only for a small range of frequency difference between the two populations and these states disappear for an increase of mismatch between the frequencies. Here the chimera-like states are characterized by the synchronized oscillations in one population and desynchronized oscillations in another population. We also find that such states observed in two distinct groups of identical populations of nonlocally coupled oscillators are different from the above case in which coexisting domains of synchronized and desynchronized oscillations are observed in one population and the second population exhibits synchronized oscillations for spatially prepared initial conditions. Perturbation from such spatially prepared initial condition leads to the existence of imperfectly synchronized states. An imperfectly synchronized state represents the existence of solitary oscillators which escape from the synchronized group in population-I and synchronized oscillations in population-II. Also the existence of chimera state is independent of the increase of frequency mismatch between the populations. We also find the coexistence of different dynamical states with respect to different initial conditions which causes multistability in the globally coupled system. In the case of nonlocal coupling, the system does not show multistability except in the cluster state region.

nlin.AO↗

arXiv2016

Two-dimensional isochronous nonstandard Hamiltonian systems

We identify a generic class of two dimensional nonstandard Hamiltonian systems which exhibit isochronous behaviour. This class of systems belongs to the two dimensional mixed Liénard- type equations and is obtained by generalizing the scalar modified Emden equation (MEE) to two dimensions. We show that the generalized class of equations admits a Hamiltonian description and exhibits periodic and quasi-periodic oscillations for suitable choice of parameters and also $\emph PT$ symmetric property.

nlin.SI↗

arXiv2016

Systems that become $\cal{PT}$ symmetric through interaction

In this article, we consider an interesting class of optical and other systems in which the interaction or coupling makes the systems to be $\cal{PT}$-symmetric. We aim to compare their dynamical behaviors with that of the usual $\cal{PT}$ symmetric systems with intrinsic loss-gain terms. In particular, we focus on the interesting non-reciprocal nature of the $\cal{PT}$ symmetric systems which has a promising application in optical diodes and optical isolators. We check whether the non-reciprocal nature is common to all $\cal{PT}$ symmetric systems and, if not, what are the situations under which it can be observed. Due to the recent interest in studying spontaneous symmetry breaking in coupled waveguide systems, we here present such symmetry breaking bifurcations in certain reciprocal and non-reciprocal $\cal{PT}$ symmetric systems.

nlin.PS↗

arXiv2016

Phase-flip chimera induced by environmental nonlocal coupling

We report the emergence of a collective dynamical state, namely phase-flip chimera, from an en- semble of identical nonlinear oscillators that are coupled indirectly via the dynamical variables from a common environment, which in turn are nonlocally coupled. The phase-flip chimera is character- ized by the coexistence of two adjacent out-of-phase synchronized coherent domains interspersed by an incoherent domain, in which the nearby oscillators are in out-of-phase synchronized states. At- tractors of the coherent domains are either from the same or different basins of attractions depending on whether they are periodic or chaotic. Conventional chimera precedes the phase-flip chimera in general. Further, the phase-flip chimera emerges after the completely synchronized evolution of the ensemble in contrast to conventional chimeras which emerge as an intermediate state between completely incoherent and coherent states. We have also characterized the observed dynamical transitions using the strength of incoherence, probability distribution of correlation coefficient and the framework of master stability function.

nlin.AO↗

arXiv2016

Imperfect synchronized states and chimera states in two interacting populations of nonlocally coupled Stuart-Landau oscillators

We investigate the emergence of different kinds of imperfect synchronized states and chimera states in two interacting populations of nonlocally coupled Stuart-Landau oscillators. We find that the complete synchronization in population-I and existence of solitary oscillators which escape from the synchronized group in population-II lead to imperfect synchronized states for sufficiently small values of nonisochronicity parameter. Interestingly, on increasing the strength of this parameter further there occurs an onset of mixed imperfect synchronized states where the solitary oscillators occur from both the populations. Synchronized oscillators from both the populations are locked to a common average frequency. In both the cases of imperfect synchronized states synchronized oscillators exhibit periodic motion while the solitary oscillators are quasi-periodic in nature. In this region, for spatially prepared initial conditions, we can observe the mixed chimera states where the coexistence of synchronized and desynchronized oscillations occur from both the populations. On the other hand, imperfect synchronized states are not always stable, and they can drift aperiodically due to instability caused by an increase of nonisochronicity parameter. We observe that these states are robust to the introduction of frequency mismatch between the two populations.

nlin.AO↗

arXiv2016

Interplay of symmetries and other integrability quantifiers in finite dimensional integrable nonlinear dynamical systems

In this work, we establish a connection between the extended Prelle-Singer procedure with other widely used analytical methods to identify integrable systems in the case of $n^{th}$-order nonlinear ordinary differential equations (ODEs). By synthesizing these methods we bring out the interlink between Lie point symmetries, contact symmetries, $λ$-symmetries, adjoint-symmetries, null forms, Darboux polynomials, integrating factors, Jacobi last multiplier and generalized $λ$-symmetries corresponding to the $n^{th}$-order ODEs. We also prove these interlinks with suitable examples. By exploiting these interconnections, the characteristic quantities associated with different methods can be deduced without solving the associated determining equations.

nlin.SI↗

arXiv2016

Different kinds of chimera death states in nonlocally coupled oscillators

We investigate the significance of nonisochronicity parameter in a network of nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We observe that the presence of nonisochronicity parameter leads to structural changes in the chimera death region while varying the strength of the interaction. This gives rise to the existence of different types of chimera death states such as multi-chimera death state, type-I periodic chimera death (PCD) state and, type-II periodic chimera death (PCD) state. We also find that the number of periodic domains in both the types of PCD states exponentially decreases with an increase of coupling range and obeys a power law under nonlocal coupling. Additionally, we also analyze the structural changes of chimera death states by reducing the system of dynamical equations to a phase model through the phase approximation. We also briefly study the role of nonisochronicity parameter on chimera states, where the existence of multi-chimera state with respect to the coupling range is pointed out. Moreover, we also analyze the robustness of the chimera death state to perturbations in the natural frequencies of the oscillators.

nlin.CD↗