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 stochastic resonance phenomenon induced by Lévy noise in a second-order and under-damped bistable system is investigated. The signal-to-noise ratio for different parameters is computed by an efficient numerical scheme. The influences of the intensity and stability index of Lévy noise, 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...

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:...

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,...