Evaluation of asymptotic characteristics of a stochastic dynamical system with event synchronization

Abstract

A model of a stochastic dynamical system with event synchronization is examined. The dynamics of the system is described by a generalized linear equation with a matrix which has one random entry on the diagonal and the other entries given by nonnegative constants related to each other by certain conditions. The problem of calculating the mean asymptotic growth rate of system state vector (the Lyapunov exponent) is considered. The solution includes change of variables resulting in new random variables instead of random state vector coordinates. It is shown that in many cases the appropriate choice of new variables reduces the problem to the study of only one sequence of random variables defined by a certain type of recurrence equation, which depends only on two of three constants in the system matrix. After constructing this sequence of random variables, the convergence of the sequence is investigated. The Lyapunov exponent is calculated as the mean value of the limiting distribution of the sequence. Refs 10. Refs 1.

Keywords:

stochastic dynamical system, Lyapunov exponent, convergence of distributions, synchronization of events