Related papers: Strong coupling yields abrupt synchronization tran…
The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally…
We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We…
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…
The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the…
In this paper, we study the applicability of an early warning index while studying the transitions to complete and generalized synchronizations in the coupled oscillator models using an unconventional system parameter and the coupling…
We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise…
Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to…
We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the…
In networks of identical linear oscillators (e.g. pendulums undergoing small vibrations) coupled through both dissipative connectors (e.g. dampers) and restorative connectors (e.g. springs) the relation between asymptotic synchronization…
Complex networks often possess communities defined based on network connectivity. When dynamics undergo in a network, one can also consider dynamical communities; i.e., a group of nodes displaying a similar dynamical process. We have…
Many real-world systems are often regarded as weakly coupled limit-cycle oscillators, in which each oscillator corresponds to a dynamical system with many degrees of freedom that have collective oscillations. One of the most practical…
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
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…
We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged.…
We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…
We study the synchronization of $N$ nearest neighbors coupled oscillators in a ring. We derive an analytic form for the phase difference among neighboring oscillators which shows the dependency on the periodic boundary conditions. At…
We investigate the stability of synchronization in networks of dynamical systems with strongly delayed connections. We obtain strict conditions for synchronization of periodic and equilibrium solutions. In particular, we show the existence…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…
Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the…