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We propose a modification of the Kuramoto model to account for the effective change in the coupling constant among the oscillators, as suggested by some experiments on Josephson junction, laser arrays and mechanical systems, where the…
We present an exemplary system of three identical oscillators in a ring interacting repulsively to show up chimera patterns. The dynamics of individual oscillators is governed by the superconducting Josephson junction. Surprisingly, the…
The instability of mixing in the Kuramoto model of coupled phase oscillators is the key to understanding a range of spatiotemporal patterns, which feature prominently in collective dynamics of systems ranging from neuronal networks, to…
We connect three phenomena in which a coherent electromagnetic field could be generated: polariton condensation, phase-locking in arrays of underdamped Josephson junctions, and lasing. All these phenomena have been described using…
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small…
The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…
Chimera states have been a vibrant subject of research in the recent past, but the analytical treatment of transitions from chimeras to coherent states remains a challenge. Here we analytically derive the necessary conditions for this…
We employ a semiclassical picture to study dynamics in a bosonic Josephson junction with various initial conditions. Phase-diffusion of coherent preparations in the Josephson regime is shown to depend on the initial relative phase between…
In this note I survey the extensive literature on the dynamics of large series arrays of identical current biased Josephson junctions coupled through various shared loads. The equations describing the dynamics are invariant under…
The critical behavior of frustrated Josephson-junction arrays at $f=1/2$ flux quantum per plaquette is considered. Results from Monte Carlo simulations and transfer matrix computations support the identification of the critical behavior of…
Recent microwave reflection measurements of Josephson junction ladders have suggested the presence of nearly coherent collective charge oscillations deep in the insulating phase. Here we develop a qualitative understanding of such coherent…
In this paper, we consider a system consisting of two capacitively coupled superconducting islands via Josephson junctions. We show that it can be reduced to two coupling harmonic oscillators under certain conditions, and solved exactly in…
Self-organized coherence-incoherence patterns, called chimera states, have first been reported in systems of Kuramoto oscillators. For coupled excitable units similar patterns, where coherent units are at rest, are called bump states. Here,…
We study the synchronization of a generalized Kuramoto system in which the coupling weights are determined by the phase differences between oscillators. We employ the fast-learning regime in a Hebbian-like plasticity rule so that the…
Interaction within an ensemble of coupled nonlinear oscillators induces a variety of collective behaviors. One of the most fascinating is a chimera state which manifests the coexistence of spatially distinct populations of coherent and…
In a network of coupled oscillators, a symmetry-broken dynamical state characterized by the coexistence of coherent and incoherent parts can spontaneously form. It is known as a chimera state. We study chimera states in a network consisting…
Chimera states, namely the coexistence of coherent and incoherent behavior, were previously analyzed in complex networks. However, they have not been extensively studied in modular networks. Here, we consider the neural network of the…
We measure the state dynamics of a tunable anharmonic quantum system, the Josephson phase circuit, under the excitation of a frequency-chirped drive. At small anharmonicity, the state evolves like a wavepacket - a characteristic response in…
Many complex systems can be represented as networks of dynamical elements whose states evolve in response to interactions with neighboring elements, noise and external stimuli. The collective behavior of such systems can exhibit remarkable…
The coherent dynamics of bubble clusters in liquid are of fundamental and industrial importance and are elusive due to the complex interactions of disordered bubble oscillations. Here we introduce and demonstrate unsupervised learning of…