Related papers: Additive noise effects in active nonlinear spatial…
We analyze the effect of pure additive noise on the long-time dynamics of the noisy Kuramoto-Sivashinsky (KS) equation in a regime close to the instability onset. We show that when the noise is highly degenerate, in the sense that it acts…
In this article we derive rigorously amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from…
We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…
Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…
A prototype model of a stochastic one-variable system with a linear restoring force driven by two cross-correlated multiplicative and additive Gaussian white noises was considered earlier [S. I. Denisov et al., Phys. Rev. E 68, 046132…
We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability…
The influence of multiplicative stochastic perturbations on the class of asymptotically Hamiltonian systems on the plane is investigated. It is assumed that disturbances do not preserve the equilibrium of the corresponding limiting system…
Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on {\em analytically-solvable}…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant…
We consider a Kuramoto-Shivashinsky like equation close to the threshold of instability with additive white noise and spatially periodic boundary conditions which simultaneously exhibit Turing bifurcations with a spatial 1:3 resonance of…
We consider the influence of stochastic perturbations on stability of a unique positive equilibrium of a difference equation subject to prediction-based control. These perturbations may be multiplicative $$x_{n+1}=f(x_n)-\left( \alpha +…
Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been…
We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Ito vs. Stratonovich), in particular in the context of noise-induced…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
We investigate the lifetime of dynamical regimes under the impact of noise motivated by low-dimensional models of the atmosphere. One may expect that the inclusion of noise tends to make the system leave prescribed regions of the state…
We present an experimental and theoretical study of the effect of spatio-temporal fluctuations in quasi-reversible systems displaying a spatial quintic supercritical bifurcation. The saturation mechanism is drastically changed by the…
We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…
Stochastic Bloch equations which model the fluorescence of two level molecules and atoms, NMR experiments and Josephson junctions are investigated to illustrate the profound effect of multiplicative noise on the critical frequency of a…
We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a…