title: Probability characteristics of nonlinear dynamical systems driven by δ-pulse noise.
abstract: For a nonlinear dynamical system described by the first-order differential equation with Poisson white noise having exponentially distributed amplitudes of δ pulses, some exact results for the stationary probability density function are derived from the Kolmogorov-Feller equation using the inverse differential operator. Specifically, we examine the "effect of normalization" of non-Gaussian noise by a linear system and the steady-state probability density function of particle velocity in the medium with Coulomb friction. Next, the general formulas for the probability distribution of the system perturbed by a non-Poisson δ-pulse train are derived using an analysis of system trajectories between stimuli. As an example, overdamped particle motion in the bistable quadratic-cubic potential under the action of the periodic δ-pulse train is analyzed in detail. The probability density function and the mean value of the particle position together with average characteristics of the first switching time from one stable state to another are found in the framework of the fast relaxation approximation.
authors.affiliation: Radiophysics Department, Lobachevsky State University, Gagarin Ave. 23, 603950 Nizhni Novgorod, Russia.
authors.forename: Alexander A
authors.initials: AA
authors.lastname: Dubkov
authors.affiliation: Radiophysics Department, Lobachevsky State University, Gagarin Ave. 23, 603950 Nizhni Novgorod, Russia.|Faculty of Physics, Lomonosov Moscow State University, Leninskie Gory, 119991 Moscow, Russia.|Prokhorov General Physics Institute, Russian Academy of Sciences, ul. Vavilova 38, 119991 Moscow, Russia.|Schmidt Institute of the Earth, Russian Academy of Sciences, ul. B. Gruzinskaya 10, 123242 Moscow, Russia.|Blekinge Institute of Technology, SE-371 Karlskrona, Sweden.
authors.forename: Oleg V
authors.initials: OV
authors.lastname: Rudenko
authors.affiliation: Radiophysics Department, Lobachevsky State University, Gagarin Ave. 23, 603950 Nizhni Novgorod, Russia.
authors.forename: Sergey N
authors.initials: SN
authors.lastname: Gurbatov