Small chimera states without multistability in a globally delay-coupled network of four lasers

Röhm, André; Böhm, Fabian; Lüdge, Kathy

doi:10.1103/physreve.94.042204

Cited by 35 publications

(24 citation statements)

References 44 publications

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“…In a co-moving frame these states are fixed points, which distinguishes them from the symmetry-broken intensity oscillations found for a small network of lasers in Ref. [46]. While a lot has been done on synchronization of Stuart-Landau oscillators [48], we could not find any references to these 'symmetrybroken amplitude-and phase-locking' states in the literature, except for Aronson et al, who found them to be always unstable [44].…”

Section: A Descriptionmentioning

confidence: 69%

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Bistability in two simple symmetrically coupled oscillators with symmetry-broken amplitude- and phase-locking

Röhm

Lüdge

Schneider

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In the model system of two instantaneously and symmetrically coupled identical Stuart-Landau oscillators, we demonstrate that there exist stable solutions with symmetry-broken amplitude- and phase-locking. These states are characterized by a non-trivial fixed phase or amplitude relationship between both oscillators, while simultaneously maintaining perfectly harmonic oscillations of the same frequency. While some of the surrounding bifurcations have been previously described, we present the first detailed analytical and numerical description of these states and present analytically and numerically how they are embedded in the bifurcation structure of the system, arising both from the in-phase and the anti-phase solutions, as well as through a saddle-node bifurcation. The dependence of both the amplitude and the phase on parameters can be expressed explicitly with analytic formulas. As opposed to the previous reports, we find that these symmetry-broken states are stable, which can even be shown analytically. As an example of symmetry-breaking solutions in a simple and symmetric system, these states have potential applications as bistable states for switches in a wide array of coupled oscillatory systems.

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Section: A Descriptionmentioning

confidence: 69%

“…[52]. As laser dynamics is a vast topic with large diversity of effects [46,53], the interplay between symmetry-broken amplitude-and phase-locking states and more complex dynamics can be explored [54].…”

Section: Discussionmentioning

confidence: 99%

Bistability in two simple symmetrically coupled oscillators with symmetry-broken amplitude- and phase-locking

Röhm

Lüdge

Schneider

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In this respect one usually adopts the notion of the so-called weak chimera states, defined by Ashwin and Burylko [54,55] as the states where two or more individuals of a system are frequency synchronized and the rest (one or more) oscillate with a different frequency than the synchronized group. Weak chimeras of this type have been numerically demonstrated in systems of three, four or sometimes a few more identical units for the cases of inertial Kuramoto model [56], Hansel-Mato-Meunier model [54] and Lang-Kobayashi-type model of delay-coupled lasers [57]; and experimentally shown in coupled pendula [58] and laser systems [59]. In this section, we shall show that the system of SQUIDS modeled by Eq.…”

Section: A Classification and Dynamics Of Possible Small Chimera Statesmentioning

confidence: 82%

Transient chaos generates small chimeras

Banerjee

Sikder

2018

Phys. Rev. E

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While the chimera states themselves are usually believed to be chaotic transients, the involvement of chaos behind their self-organization is not properly distinguished or studied. In this work, we demonstrate that small chimeras in the local flux dynamics of an array of magnetically coupled superconducting quantum interference devices (SQUIDs) driven by an external field are born through transiently chaotic dynamics. We deduce analytic expressions for small chimeras and synchronous states which correspond to nonchaotic attractors in the model. We also numerically study the bifurcations underlying the multistability responsible for their generation. Transient chaos manifests itself in the short term flux oscillations with erratically fluctuating amplitudes, exponential escape time distribution and irregular dependence of the escape time to initial conditions. We classify the small chimera states in terms of the position of the non-synchronized member and numerically construct their basin of attraction. The basin is shown to possess an interesting structure consisting of both ordered and fractal parts, which again can be attributed to transient chaos.

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“…(1). Equations (13), (14), and (16) only tell which of those states are possible; they do not indicate what initial conditions in the GCM system will conduce to those particular states. As it is typical of cluster and chimera states in systems of coupled oscillators, the predicted states in the autonomous GCM system depend on initial conditions.…”

Section: Spatiotemporal Patterns For Asymmetric Cluster and Chimermentioning

confidence: 99%

Asymmetric cluster and chimera dynamics in globally coupled systems

Cano

Cosenza

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate the emergence of chimera and cluster states possessing asymmetric dynamics in globally coupled systems, where the trajectories of oscillators belonging to different subpopulations exhibit different dynamical properties. In an asymmetric chimera state, the trajectory of an element in the synchronized subset is stationary or periodic, while that of an oscillator in the desynchronized subset is chaotic. In an asymmetric cluster state, the periods of the trajectories of elements belonging to different clusters are different. We consider a network of globally coupled chaotic maps as a simple model for the occurrence of such asymmetric states in spatiotemporal systems. We employ the analogy between a single map subject to a constant drive and the effective local dynamics in the globally coupled map system to elucidate the mechanisms for the emergence of asymmetric chimera and cluster states in the latter system. By obtaining the dynamical responses of the driven map, we establish a condition for the equivalence of the dynamics of the driven map and that of the system of globally coupled maps. This condition is applied to predict parameter values and subset partitions for the formation of asymmetric cluster and chimera states in the globally coupled system.Recently a fascinating phenomenon occurring in networks of coupled identical oscillators has attracted much attention from researchers in various fields: chimera states. A chimera state consists of the simultaneous coexistence of subsets of oscillators with synchronous (coherent) and asynchronous (incoherent) dynamics. This behavior represents a state of broken synchronization symmetry and has been studied theoretically and experimentally in different contexts and also with a variety of coupling schemes. In systems with global interactions, chimera states are related to the formation of clusters, where the system segregates into distinguishable subsets of synchronized elements. Here we investigate the emergence of chimera states possessing asymmetric dynamics, in the sense that the dynamical evolution of oscillators belonging to the synchronized or the desynchronized subset are different: the trajectory shared by the oscillators in the synchronized subset is stationary, while that of an oscillator in the desynchronized subset is chaotic. Similarly, we investigate asymmetric cluster states, where the periods of the orbits of oscillators belonging to different clusters are different. In particular, the coexistence of synchronized and desynchronized subsets possessing asymmetric dynamics represents a further breaking of the synchronization symmetry in a system of coupled identical oscillators.

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Small chimera states without multistability in a globally delay-coupled network of four lasers

Cited by 35 publications

References 44 publications

Bistability in two simple symmetrically coupled oscillators with symmetry-broken amplitude- and phase-locking

Bistability in two simple symmetrically coupled oscillators with symmetry-broken amplitude- and phase-locking

Transient chaos generates small chimeras

Asymmetric cluster and chimera dynamics in globally coupled systems

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