This paper is devoted to investigate the stochastic stationary responses of a viscoelastic system with impacts under additive Gaussian white noise excitation. First, the viscoelastic force is approximated as equivalent stiffness and damping terms, and the original system is replaced by a system...

In this paper, a stochastic system with correlation between non-Gaussian noise and Gaussian colored noise is investigated. We carry out the functional methods to derive the approximate Fokker–Planck equation, and the expressions of stationary probability density function and mean first-passage...

The present paper is devoted to the numerical solution of the Fokker–Planck (FP) equation associated to the Duffing oscillator driven by colored noise. We propose an improved discretization of the standard FP operator-splitting method which renders the scheme unconditionally stable. This...

The stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative and additive noise when the additive noise is a linear combination of an asymmetric dichotomous noise and its square. The exact expressions are obtained for the first two moments and the correlation...

This paper is to continue our study on complex beam–beam interaction models in particle accelerators with random excitations Y. Xu, W. Xu, G.M. Mahmoud, On a complex beam–beam interaction model with random forcing [Physica A 336 (2004) 347–360]. The random noise is taken as the form of...

In recent years, many studies have been devoted to complex differential equations (CDE), which appear in very important applications in physics and engineering. This paper aims to investigate one such CDE, containing a random forcing term:...

The relaxation time Tc of the intensity correlation function is investigated in a single-mode dye laser system driven by cross-correlated additive and multiplicative white noises. The expression for Tc is obtained by using the projector–operator method. And then the effects of correlation...

In this paper, we consider the phenomenon of stochastic resonance (SR) in an asymmetric bistable system with coloured noises and periodic rectangular signal. Expression of the signal-to-noise ratio (SNR) has been obtained under the adiabatic limit. We investigate the effect of any system...

In the present paper, a class of stochastic time-delayed systems driven by correlated Gaussian white noises are considered. Novikov’s theorem is used to derive delay Fokker–Planck equations. In the case of small time delays, approximate stationary solutions are obtained. As a special case,...

The transient and stationary probability density functions (PDFs) of stochastic response of the ϕ6 Duffing oscillator under combined harmonic and external and parametric Poisson white noises excitations are investigated by the generalized cell mapping method in this paper. Based on the digraph...