Related papers: Phase Reduction Method for Strongly Perturbed Limi…
Multirhythmicity, a form of multistability, in an oscillator is an intriguing phenomenon found across many branches of science. From an application point of view, while the multirhythmicity is sometimes desirable as it presents us with many…
Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are "sufficiently weak", an assumption that is not always…
We introduce a simple model system to study synchronization theoretically in quantum oscillators that are not just in limit-cycle states, but rather display a more complex bistable dynamics. Our oscillator model is purely dissipative, with…
The dynamics of an ensemble of $N$ weakly coupled limit-cycle oscillators can be captured by their $N$ phases using standard phase reduction techniques. However, it is a phenomenological fact that all-to-all strongly coupled limit-cycle…
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly…
We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture,…
When a driven oscillator loses phase-locking to a master oscillator via a Hopf bifurcation, it enters a bounded-phase regime in which its average frequency is still equal to the master frequency, but its phase displays temporal…
We study the influence of telegraph noise on synchrony of limit cycle oscillators. Adopting the phase description for these oscillators, we derive the explicit expression for the Lyapunov exponent. We show that either for weak noise or…
A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations…
We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters which measure synchronization of phases and frequencies are introduced and analyzed by means of dynamic simulations…
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 review the conventional phase-locking technique in the long-term stabilization of the mode-locked fiber laser and investigate the phase noise limitation of the conventional technique. To break the limitation, we propose an improved…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions:…
We investigate synchronization effects in quantum self-sustained oscillators theoretically using the micromaser as a model system. We use the probability distribution for the relative phase as a tool for quantifying the emergence of…
By spreading phases on the unit circle, desynchronization algorithm is a powerful tool to achieve round-robin scheduling, which is crucial in applications as diverse as media access control of communication networks, realization of…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
In this letter, we present an elegant method to build and maintain an anti-phase configuration of two nonlinear oscillators with different natural frequencies and dynamics described by the sinusoidal phase-reduced model. The anti-phase…