Combined effects of additive and multiplicative noise in a Fokker-Planck model

1987 ◽  
Vol 66 (2) ◽  
pp. 263-269 ◽  
Author(s):  
J. J. Brey ◽  
J. M. Casado ◽  
M. Morillo
Keyword(s):  
Multiplicative Noise ◽  
Combined Effects ◽  
Additive And Multiplicative Noise ◽  
Fokker Planck

scholarly journals Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1329
Author(s):  
Lev Ryashko ◽  
Dmitri V. Alexandrov ◽  
Irina Bashkirtseva
Keyword(s):  
Multiplicative Noise ◽  
Nonlinear Dynamical Systems ◽  
Stochastic Theory ◽  
Slow Variable ◽  
Theoretical Description ◽  
Mathematical Study ◽  
Stochastic Generation ◽  
Nonlinear Dynamical ◽  
Additive And Multiplicative Noise ◽  
And Shifts

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

scholarly journals GPS Signal Detection under Multiplicative and Additive Noise

2012 ◽  
Vol 66 (4) ◽  
pp. 479-500 ◽  
Author(s):  
P. Huang ◽  
Y. Pi ◽  
I. Progri
Keyword(s):  
Signal Detection ◽  
Urban Areas ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Power Level ◽  
Signal Propagation ◽  
Signal Acquisition ◽  
Detection Scheme ◽  
Additive And Multiplicative Noise ◽  
Gps Signal Acquisition

In some Global Positioning System (GPS) signal propagation environments, especially in the ionosphere and urban areas with heavy multipath, GPS signal encounters not only additive noise but also multiplicative noise. In this paper we compare and contrast the conventional GPS signal acquisition method which focuses on handling GPS signal acquisition with additive noise, with the enhanced GPS signal processing under multiplicative noise by proposing an extension of the GPS detection mechanism, to include the GPS detection model that explains detection of the GPS signal under additive and multiplicative noise. For this purpose, a novel GPS signal detection scheme based on high order cyclostationarity is proposed. The principle is introduced, the GPS signal detection structure is described, the ambiguity of initial PseudoRandom Noise (PRN) code phase and Doppler shift of GPS signal is analysed. From the simulation results, the received GPS signal at low power level, which is degraded by additive and multiplicative noise, can be detected under the condition that the received block of GPS data length is at least 1·6 ms and sampling frequency is at least 5 MHz.

scholarly journals Collisional Evolution of Galaxy Clusters: Fokker–Planck and N-body models

2003 ◽  
Vol 208 ◽  
pp. 449-450
Author(s):  
Koji Takahashi ◽  
Tomohiro Sensui ◽  
Yoko Funato ◽  
Junichiro Makino
Keyword(s):  
Power Law ◽  
Dynamical Evolution ◽  
Cluster Center ◽  
Combined Effects ◽  
Clusters Of Galaxies ◽  
Relative Importance ◽  
Self Consistent ◽  
The Common ◽  
Good Agreement ◽  
Fokker Planck

We investigate the dynamical evolution of clusters of galaxies in virial equilibrium by using Fokker–Planck models and self-consistent N-body models. In particular we focus on the growth of the common halos and the development of the central density cusps in the clusters. We find good agreement between the Fokker–Planck and N-body models. At the cluster center the cusp approximated by a power law, ρ(r) ∝ r-α (α ∼ 1), develops. We conclude that this shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness α weakly depends on the relative importance of tidal stripping.

scholarly journals Nonparametric estimation in a regression model with additive and multiplicative noise

2020 ◽  
Vol 380 ◽  
pp. 112971 ◽  
Author(s):  
Christophe Chesneau ◽  
Salima El Kolei ◽  
Junke Kou ◽  
Fabien Navarro
Keyword(s):  
Regression Model ◽  
Nonparametric Estimation ◽  
Multiplicative Noise ◽  
Additive And Multiplicative Noise

scholarly journals Linking Nonlinearity and Non-Gaussianity of Planetary Wave Behavior by the Fokker–Planck Equation

2005 ◽  
Vol 62 (7) ◽  
pp. 2098-2117 ◽  
Author(s):  
Judith Berner
Keyword(s):  
Stochastic Model ◽  
Probability Density ◽  
Planetary Wave ◽  
Multiplicative Noise ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
State Dependent ◽  
Nonlinear Stochastic Model ◽  
Non Gaussian ◽  
Fokker Planck

Abstract To link prominent nonlinearities in the dynamics of 500-hPa geopotential heights to non-Gaussian features in their probability density, a nonlinear stochastic model of atmospheric planetary wave behavior is developed. An analysis of geopotential heights generated by extended integrations of a GCM suggests that a stochastic model and its associated Fokker–Planck equation call for a nonlinear drift and multiplicative noise. All calculations are carried out in the reduced phase space spanned by the leading EOFs. It is demonstrated that this nonlinear stochastic model of planetary wave behavior captures the non-Gaussian features in the probability density function of atmospheric states to a remarkable degree. Moreover, it not only predicts global temporal characteristics, but also the nonlinear, state-dependent divergence of state trajectories. In the context of this empirical modeling, it is discussed on which time scale a stochastic model is expected to approximate the behavior of a continuous deterministic process. The reduced model is then used to determine the importance of the nonlinearities in the drift and the role of the multiplicative noise. While the nonlinearities in the drift are crucial for a good representation of planetary wave behavior, multiplicative (i.e., state dependent) noise is not absolutely essential. It is found that a major contributor to the stochastic component is the Branstator–Kushnir oscillation, which acts as a fluctuating force for physical processes with even longer time scales, like those that project on the Arctic Oscillation pattern. In this model, the oscillation is represented by strongly correlated noise.

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