We have studied the stochastic resonance (SR) of bistable systems coupled to a bath with a nonlinear system–bath interaction, by using the microscopic, generalized Caldeira–Leggett (CL) model. The adopted CL model yields the non-Markovian Langevin equation with nonlinear dissipation and...

The stochastic resonance (SR) of periodically driven linear system with multiplicative white noise and periodically modulated additive white noise is studied. Exact expressions of output signal-to-noise ratio are obtained. The SR characteristics features are shown in two different situations:...

We show that non-linear diffusion equations can describe state-dependent diffusion, i.e., fission–fusion dynamics. We thereby provide a new dynamical basis for understanding Tsallis distributions (q-Gaussian distributions), anomalous diffusion (subdiffusion, superdiffusion and superballistic...

Parameter-induced aperiodic stochastic resonance (SR) in the presence of multiplicative and additive noise is investigated in detail. Using theoretical and numerical analysis, we evaluate the dynamical probability density, by which the bit error rate is defined as a quantity to optimize in the...

We compute the characteristic functional of a nonlinear transformation of a set of random variables. The equation is applied to the study of fractal stochastic processes with multiplicative noise. For illustration we investigate two types of chemical systems subjected to environmental...

We address the issue of edge detection in Synthetic Aperture Radar imagery. In particular, we propose nonparametric methods for edge detection, and numerically compare them to an alternative method that has been recently proposed in the literature. Our results show that some of the proposed...

We consider the Langevin lattice dynamics for a spontaneously broken λϕ4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg–Landau–Langevin and the subtleties related to the...

We study a generalised model of population growth in which the state variable is population growth rate instead of population size. Stochastic parametric perturbations, modelling phenotypic variability, lead to a Langevin system with two sources of multiplicative noise. The stationary...

We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate rδ, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r>rδ corresponds...</1,>

Using the Euler–Maruyama numerical method, we present calculations of the Ermakov–Lewis invariant and the dynamic, geometric, and total phases for several cases of stochastic parametric oscillators, including the simplest case of the stochastic harmonic oscillator. The results are compared...