Related papers: Noise-induced bifurcations, Multiscaling and On-Of…
We study analytically and numerically the noise-induced transition between an absorbing and an oscillatory state in a Duffing oscillator subject to multiplicative, Gaussian white noise. We show in a non-perturbative manner that a stochastic…
We derive the exact bifurcation diagram of the Duffing oscillator with parametric noise thanks to the analytical study of the associated Lyapunov exponent. When the fixed point is unstable for the underlying deterministic dynamics, we show…
We study noise induced switching in systems far from equilibrium by using an underdamped micromechanical torsional oscillator driven into the nonlinear regime. Within a certain range of driving frequencies, the oscillator possesses two…
A bifurcating system subject to multiplicative noise can display on-off intermittency. Using a canonical example, we investigate the extreme sensitivity of the intermittent behavior to the nature of the noise. Through a perturbative…
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…
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…
A bifurcating system subject to multiplicative noise can exhibit on-off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the…
We demonstrate that nonlocally coupled limit-cycle oscillators subject to spatiotemporally white Gaussian noise can exhibit a noise-induced transition to turbulent states. After illustrating noise-induced turbulent states with numerical…
Unidirectionally coupled dynamical system is studied by focusing on the input (or boundary) dependence. Due to convective instability, noise at an up-flow is spatially amplified to form an oscillation. The response, given by the down-flow…
One of the models of intermittency is on-off intermittency, arising due to time-dependent forcing of a bifurcation parameter through a bifurcation point. For on-off intermittency the power spectral density of the time-dependent deviation…
We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of Stochastic Resonance. We present a…
The effect of multiplicative stochastic perturbations on Hamiltonian systems on the plane is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium of the limiting system. The paper investigates…
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…
We report a noise induced delay of bifurcation in a simple pulse-coupled neural circuit. We study the behavior of two neural oscillators, each individually governed by saddle-node dynamics, with reciprocal excitatory synaptic connections.…
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…
A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be…
We prove the existence of multiple noise-induced transitions in the Lasota-Mackey map, which is a class of one dimensional random dynamical system with additive noise. The result is achieved by the help of rigorous computer assisted…
We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…
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…
The influence of multiplicative white noise on the resonance capture of strongly nonlinear oscillatory systems under chirped-frequency excitations is investigated. It is assumed that the intensity of the perturbation decays polynomially…