Related papers: Colored noise in Spatially-Extended Systems
The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two…
We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a…
A system with two correlated Gaussian white noises is analysed. This system can describe both stochastic localization and long tails in the stationary distribution. Correlations between the noises can lead to a nonmonotonic behaviour of the…
The interaction between solid-state qubits and their environmental degrees of freedom produces non-unitary effects like decoherence and dissipation. Uncontrolled decoherence is one of the main obstacles that must be overcome in quantum…
We characterize the influence that external noise, with both spatial and temporal correlations, has on the scale dependence of the reaction parameters of a cubic autocatalytic reaction diffusion (CARD) system. Interpreting the CARD model as…
We characterize a stochastic dynamical system with tempered stable noise, by examining its probability density evolution. This probability density function satisfies a nonlocal Fokker-Planck equation. First, we prove a superposition…
The effects of spatially correlated noise on a phenomenological equation equivalent to a non-local version of the Kardar-Parisi-Zhang equation are studied via the dynamic renormalization group (DRG) techniques. The correlated noise coupled…
The dynamics of well-mixed biological populations is usually studied by mean-field methods and weak-noise expansions. Similar methods have been applied also in spatially extended problems, relying on the fact that these populations are…
We analytically derive the correlation functions of the stochastic response of period-p orbits in a generic one-dimensional map system under the influence of weak external, additive white noise. Two approaches, a recurrence scheme and a…
We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with…
Stationary solutions to a Fokker-Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an…
We treat analytically a model that captures several features of the phenomenon of spatially inhomogeneous reversal of an order parameter. The model is a classical Ginzburg-Landau field theory restricted to a bounded one-dimensional spatial…
Interactions in active matter systems inherently involve delays due to information processing and actuation lags. We numerically investigate the impact of such delays on the phase behavior of the Vicsek model for motile active matter at a…
We study the influence of off-diagonal harmonic noise on transitions in a Landau-Zener model. We demonstrate that the harmonic noise can change the transition probabilities substantially and that its impact depends strongly on the…
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…
The synchrony and variability have been discussed of the coupled Langevin model subjected to spatially correlated additive and multiplicative noise. We have employed numerical simulations and the analytical augmented-moment method which is…
Statistical averaging theorems allow us to derive a set of equations for the averaged magnetization dynamics in the presence of colored (non-Markovian) noise. The non-Markovian character of the noise is described by a finite…
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…
The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as…
The Tsallis entropy and Fisher information entropy (matrix) are very important quantities expressing information measures in nonextensive systems. Stationary and dynamical properties of the information entropies have been investigated in…