Related papers: Noise activated switching in a driven, nonlinear m…

Additive noise is known to produce counter-intuitive behaviors in nonlinear dynamical systems. Previously, it was shown that systems with a deterministic limit cycle can display bistable switching between metastable states in the presence…

The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears.…

This book chapter describes the dynamics of a modulated oscillator for resonant and nonresonant modulation. Two types of resonant modulation are considered: additive, with frequency close to the oscillator eigenfrequency, and parametric,…

We study switching between period-two states of an underdamped quantum oscillator modulated at nearly twice its natural frequency. For all temperatures and parameter values switching occurs via quantum activation: it is determined by…

We consider escape from a metastable state of a nonlinear oscillator driven close to triple its eigenfrequency. The oscillator can have three stable states of period-3 vibrations and a zero-amplitude state. Because of the symmetry of…

We study the stationary and nonstationary measurement of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. For this purpose, we develop a theoretical framework based on the…

We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise…

A new type of noised-induced phase transitions that should occur in systems of elements with motivated behavior is considered. By way of an example, a simple oscillatory system {x,v} with additive white noise is analyzed numerically. A…

The dynamical control of energy transfer between interacting systems is fundamental in diverse applications related to physical, electronic and chemical processes. Recent developments show that noise may enhance or suppress power transfer…

We consider a generic class of gene circuits affected by nonlinear extrinsic noise. To address this nonlinearity we introduce a general perturbative methodology based on assuming timescale separation between noise and genes dynamics, with…

Here we study a noise induced transition when the system is driven by a noise source taken as colored and non-Gaussian. We show--using both, a theoretical approximation and numerical simulations-- that there is a shift of the transition as…

We consider a nonlinear oscillator with state-dependent time-delay that displays a countably infinite number of nested limit cycle attractors, \emph{i.e.} megastability. In the low-memory regime, the equation reduces to a self-excited…

The nonlinear response of noisy bistable systems driven by strong amplitude periodical force is investigated by physical experiment. The new phenomenon of locking of the mean switching frequency between states of bistable system is found.…

Intrinsic or demographic noise has been shown to play an important role in the dynamics of a variety of systems including predator-prey populations, intracellular biochemical reactions, and oscillatory chemical reaction systems, and is…

We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical…

The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillations regime and the excitable one are described. The first regime consists in the coexistence of two stable limit cycles in the phase…

Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…

We study the fluctuation-activated transition process in a system of two coupled bistable oscillators, in which each oscillator is driven by one constant force and an independent Gaussian white noise. The transition pathway has been…

We introduce an extension to the standard reduction of oscillatory systems to a single phase variable. The standard reduction is often insufficient, particularly when the oscillations have variable amplitude and the magnitude of each…

We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting…