Probability characteristics of nonlinear dynamical systems driven by δ -pulse noise
- Post by: Tobias Larsson
- 17th June 2016
- No Comment
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.
KEYWORDS
Differential equations; Dynamical systems; Gaussian noise (electronic); Linear systems; Mathematical operators; Nonlinear dynamical systems; Nonlinear equations; Poisson distribution; Poisson equation; Probability; Probability distributions; Velocity control; White noise, Differential operators; First order differential equation; Non-Gaussian noise; Overdamped particles; Particle velocities; Stationary probability density function; Steady state probabilities; System trajectory, Probability density function
CITATION
Alexander A. Dubkov, Oleg V. Rudenko, and Sergey N. Gurbatov. Probability characteristics of nonlinear dynamical systems driven by δ-pulse noise. Phys. Rev. E 93, 062125 – Published 17 June 2016. DOI: 10.1103/PhysRevE.93.062125
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http://urn.kb.se/resolve?urn=urn:nbn:se:bth-12776