STABILITY OF STOCHASTIC SYSTEMS WITH MEMORY

Abstract

Many processes in physics, biology, ecology, mechanics etc. can be modeled by Volterra integro-differential equations (VIDEs) with "fading memory". Often the behaviour of corresponding systems is perturbed by random noises. One of the main problems for the theory of stochastic Volterra integro-differential equations (SVIDEs) is connected with their stability. The present paper is devoted to the numerical solution of the stability problem for linear SVIDEs. The method is based on the statistical simulation of input random wide-band stationary processes, which are assumed in the form of "colored" noises. For each realization the numerical solution of VIDEs is found. The conclusion about the stability of the considered system SVIDE with respect to statistical moments is made on the basis of Liapunov exponents, which are calculated for statistical moments of the solution.