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We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous…
We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. We focus on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone. Comparing the synchronization properties…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical…
Nonlinear dynamical systems possessing an invariant subspace in the phase space and chaotic or stochastic motion within the subspace often display on-off intermittency close to the threshold of stability of the subspace. In a class of…
The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodical force is combined with a theoretical analysis by means of the quasi-harmonic…
Synchronous oscillatory dynamics is frequently observed in the human brain. We analyze the fine temporal structure of phase-locking in a realistic network model and match it with the experimental data from parkinsonian patients. We show…
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been…
We investigate topological and spectral properties of models of European and US-American power grids and of paradigmatic network models as well as their implications for the synchronization dynamics of phase oscillators with heterogeneous…
We study, both analytically and numerically, the dynamics of mechanical oscillators kept in motion by a feedback force, which is generated electronically from a signal produced by the oscillators themselves. This kind of self-sustained…
We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback…
We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e.,…
We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean…
Experimental exploration of synchronization in scalable oscillator micro systems has unfolded a deeper understanding of networks, collective phenomena, and signal processing. Cavity optomechanical devices have played an important role in…
We investigate the quantum synchronization dynamics of a moving qubit interacting with a dissipative cavity environment, using the Husimi $Q$-function to analyze its phase space evolution. Unlike conventional synchronization between…
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…