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 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...

Global analysis of bifurcation in the Duffing–van der Pol oscillators under both additive and multiplicative random excitations is explored in detail by the generalized cell mapping method using digraph. System parameters are chosen in the range that two co-exist attractors and a saddles. As...

The aim of this paper is to continue our previous investigations on beam–beam interaction models in particle accelerators by considering these models under narrow-band random excitation. In this investigation the multiple scale and the moment methods are used. The equations of modulation of...

The main topic of this paper is the study of the stationary solution of a stochastically complex dynamical system. The stochastic averaging method of quasi-Hamiltonian system, an important tool for the analysis of dynamical properties of stochastically real dynamical system, is used at the first...

This paper aims to investigate the stationary probability density functions (PDFs) of a Duffing–Van der Pol vibro-impact system excited by correlated Gaussian white noise. With the help of non-smooth transformation, the stationary PDFs are formulated analytically by the stochastic averaging of...

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:...