Related papers: Phase reduction approach to synchronization of non…
Limit-cycle oscillators are the basic building blocks for synchronization; yet, the notion of a quantum limit cycle has remained unclear. Here, we study quantum limit cycles and synchronization in the presence of continuous heterodyne…
Phase-locked solutions of coupled oscillators are studied with asymmetric coupling strengths or inhomogeneous natural frequencies. The solutions show remarkable profiles of phase lags from the pacemaker corresponding to the ratio of upward…
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…
Oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. The standard phase reduction, a model reduction technique based on isochrons, can be unsuitable for…
The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the…
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…
We study phase synchronization for a ratchet system. We consider the deterministic dynamics of a particle in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in…
The paper documents the implementation of a novel phase-noise analysis module within the open-source QUCS circuit simulator environment. The underlying algorithm is based on a rigorous, unified time-domain methodology of (coupled)…
We study the properties of large systems of globally coupled oscillators in the presence of noise. When the distribution of the natural frequencies of the oscillators is bimodal and its analytical continuation in the complex plane has only…
Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with…
We study the manifestation of antiphase synchronization in a system of n Rossler Oscillators coupled through a dynamic environment. When the feedback from system to environment is positive (negative) and that from environment to system is…
The synchronization analysis of limit-cycle oscillators is prevalent in many fields, including physics, chemistry, and life sciences. It relies on the phase calculation that utilizes measurements. However, the synchronization of…
Low-dimensional reduction theories, such as the Ott-Antonsen ansatz, have played a crucial role in the study of populations of globally coupled phase oscillators. However, most of these theories are applicable only to models in which the…
Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic…
Synchronization of forced reactively coupled van der Pol oscillators is investigated in the phase approximation. We discuss essential features of the reactive coupling. Bifurcation mechanisms for the destruction of complete synchronization…
We examine microscopic mechanisms for coupling stochastic oscillators so that they display similar and correlated temporal variations. Unlike oscillatory motion in deterministic dynamical systems, complete synchronization of stochastic…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
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,…