On the hysteretic operators with random parameters

Abstract

In this work we introduce the novel class of hysteretic operators with random parameters. We consider the definition of these operators in terms of the “input-output” relations, namely: for all permissible continuous inputs corresponds the output in the form of stochastic Markovian process. The properties of such operators are also considered and discussed on the example of a non-ideal relay with random parameters. Application of hysteretic operators with stochastic parameters is demonstrated on the example of simple oscillating system and the results of numerical simulations are presented.