Related papers: Low-dimensional dynamics of phase oscillators driv…
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…
We consider the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, containing a folded-node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations,…
Many biological and physical systems exhibit population-density dependent transitions to synchronized oscillations in a process often termed "dynamical quorum sensing". Synchronization frequently arises through chemical communication via…
We present simulations and a theoretical treatment of vertically vibrated granular media. The systems considered are confined in narrow quasi-two-dimensional and quasi-one-dimensional (column) geometries, where the vertical extension of the…
First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of…
We outline formal and physical similarities between the quantum dynamics of open systems, and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, that,…
Natural dynamics is often dominated by sudden nonlinear processes such as neuroavalanches, gamma-ray bursts, solar flares \emph{etc}. that exhibit scale-free statistics much in the spirit of the logarithmic Ritcher scale for earthquake…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the…
We study the effects of noise cross-correlations on the steady states of driven, nonequilibrium systems, which are described by two stochastically driven dynamical variables, in one dimension. We use a well-known stochastically driven…
The Kuramoto model has become a paradigm to describe the dynamics of nonlinear oscillator under the influence of external perturbations, both deterministic and stochastic. It is based on the idea to describe the oscillator dynamics by a…
Recently, several studies have investigated synchronization in quantum-mechanical limit-cycle oscillators. However, the quantum nature of these systems remained partially hidden, since the dynamics of the oscillator's phase was overdamped…
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…
This paper investigates the effect of oscillator phase noise and channel variations due to fading on the performance of communication systems at frequency bands higher than 10GHz. Phase noise and channel models are reviewed and…
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…
In the present paper, we consider a Cauchy problem for a linear second order in time abstract differential equation with pure delay. In the absence of delay, this problem, known as the harmonic oscillator, has a two-dimensional eigenspace…
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 address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First,…
We explore identical R\"ossler systems organized into two equally-sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. Patterns of distinctly synchronized phase dynamics are observed, which…
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
We study the onset of collective oscillations at low temperature in a three-dimensional spin model with non-reciprocal short-range interactions. Performing numerical simulations of the model, the presence of a continuous phase transition to…