Analytical approach to synchronous states of globally coupled noisy rotators

Munyaev, V. O.; Smirnov, L. A.; Kostin, V. A.; Osipov, Grigory V.; Pikovsky, Arkady

doi:10.1088/1367-2630/ab6f93

Cited by 13 publications

(3 citation statements)

References 24 publications

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“…Indeed, simple energy considerations show (Supplementary Information) that the laser power threshold for synchronization should increase with temperature. A regime of synchronization in an ensemble of globally coupled phase oscillators with distributed intrinsic oscillator frequencies and external independent noise forces-a system closer to the present experiment-has also been investigated, indicating a non-equilibrium transition between desynchronized and synchronized states and the existence of bistability 25,26 .…”

Section: Discussionsupporting

confidence: 56%

Photonic metamaterial analogue of a continuous time crystal

Liu

MacDonald

et al. 2023

Nat. Phys.

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Time crystals are an eagerly sought phase of matter with broken time-translation symmetry. Quantum time crystals with discretely broken time-translation symmetry have been demonstrated in trapped ions, atoms and spins whereas continuously broken time-translation symmetry has been observed in an atomic condensate inside an optical cavity. Here we report that a classical metamaterial nanostructure, a two-dimensional array of plasmonic metamolecules supported on flexible nanowires, can be driven to a state possessing all of the key features of a continuous time crystal: continuous coherent illumination by light resonant with the metamolecules’ plasmonic mode triggers a spontaneous phase transition to a superradiant-like state of transmissivity oscillations, resulting from many-body interactions among the metamolecules, characterized by long-range order in space and time. The phenomenon is of interest to the study of dynamic classical many-body states in the strongly correlated regime and applications in all-optical modulation, frequency conversion and timing.

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Section: Discussionsupporting

confidence: 56%

Photonic metamaterial analogue of a continuous time crystal

Liu

MacDonald

et al. 2023

Nat. Phys.

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“…We concentrated on the popular 'standard' models of coupled oscillators. One of the possible extensions could be exploring other systems with a disorder in the coupling, which in the ordered case demonstrate a transition to synchrony, such as active rotators [33][34][35], phase oscillators 'with inertia' described by the second-order equations [36][37][38], higher-dimensional generalizations of the Kuramoto model [20,[39][40][41][42]. While disorder in the phase shifts is quite natural for phase oscillators (and other oscillators with a well-defined phase), a corresponding formulation for pulse-coupled units like neurons [43][44][45] is another challenging task for future studies.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of oscillator populations with disorder in the coupling phase shifts

Pikovsky,

Bagnoli

2024

New J. Phys.

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We study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific order as the coupling strength increases. This order is characterized by partial phase locking, which is put into evidence by the introduced novel correlation order parameter, which is shown to grow monotonically with the coupling strength, and via frequency entrainment by following concentration of the oscillators frequencies. Simulations with phase oscillators, Stuart–Landau oscillators, and chaotic Roessler oscillators demonstrate similar scaling of the correlation order parameter with the coupling and the system size and also similar behavior of the frequencies with maximal entrainment (at which the standard deviation of the frequencies is reduced by a factor close to four) at some finite coupling.

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“…The inclusion of inertia yields two-dimensional intrinsic oscillator dynamics, thereby making the cooperative dynam-ics of the second-order Kuramoto model substantially more complex than of its classical first-order counterpart. These inertia-induced dynamics include complex and hysteretic transitions from incoherence to full synchronization [37][38][39][40][41][42][43], bistability of synchronous clusters [44], chaotic inter-cluster dynamics [45], chimeras [46][47][48], and solitary states [49,50]. Solitary states emerge in a network at the edge of full synchronization when all but one oscillator synchronize in a synchronous cluster, while the remaining, "solitary" oscillator has either a constant phase shift with respect to the synchronous cluster or rotates with a different frequency.…”

Section: Introductionmentioning

confidence: 99%

Stability of rotatory solitary states in Kuramoto networks with inertia

Munyaev,

Bolotov,

Smirnov

et al. 2021

Preprint

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Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and becomes incoherent with the rest of the network. Such chimera-type patterns with an incoherent state formed by a single oscillator were observed in various oscillator networks; however, there is still a lack of understanding of how such states can stably appear. Here, we study the stability of solitary states in Kuramoto networks of identical two-dimensional phase oscillators with inertia and a phase-lagged coupling. The presence of inertia can induce rotatory dynamics of the phase difference between the solitary oscillator and the coherent cluster. We derive asymptotic stability conditions for such a solitary state as a function of inertia, network size, and phase lag that may yield either attractive or repulsive coupling. Counterintuitively, our analysis demonstrates that (i) increasing the size of the coherent cluster can promote the stability of the solitary state in the attractive coupling case and (ii) the solitary state can be stable in small-size networks with all repulsive coupling. We also discuss the implications of our stability analysis for the emergence of rotatory chimeras.

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Analytical approach to synchronous states of globally coupled noisy rotators

Cited by 13 publications

References 24 publications

Photonic metamaterial analogue of a continuous time crystal

Photonic metamaterial analogue of a continuous time crystal

Dynamics of oscillator populations with disorder in the coupling phase shifts

Stability of rotatory solitary states in Kuramoto networks with inertia

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