Related papers: Slow-fast dynamics of strongly coupled adaptive fr…
We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…
We study collective behavior of locally coupled limit-cycle oscillators with random intrinsic frequencies, spatially extended over $d$-dimensional hypercubic lattices. Phase synchronization as well as frequency entrainment are explored…
Intermittent synchronization is observed in a variety of different experimental settings in physics and beyond and is an established research topic in nonlinear dynamics. When coupled oscillators exhibit relatively weak, intermittent…
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…
A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical…
Synchronization of network-coupled dynamical units is important to a variety of natural and engineered processes including circadian rhythms, cardiac function, neural processing, and power grids. Despite this ubiquity, it remains poorly…
Synchronization in quantum systems has been recently studied through persistent oscillations of local observables, which stem from undamped modes of the dissipative dynamics. However, the existence of such modes requires fine-tuning the…
If an oscillator is driven by a force that switches between two frequencies, the dynamics it exhibits depends on the precise manner of switching. Here we take a one-dimensional oscillator and consider scenarios in which switching occurs:…
Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for…
We study dynamics of phase-differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…
The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator…
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…
We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…
We study a family of dynamical systems obtained by coupling an Anosov map on the two-dimensional torus -- the chaotic system -- with the identity map on the one-dimensional torus -- the neutral system -- through a dissipative interaction.…
Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously when they are strongly…
This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of…
The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase…
We present a method to infer network connectivity from collective dynamics in networks of synchronizing phase oscillators. We study the long-term stationary response to temporally constant driving. For a given driving condition, measuring…