Stationary Response of a Class of Nonlinear Stochastic Systems Undergoing Markovian Jumps

Abstract

Systems whose specifications change abruptly and statistically, referred to as Markovianjump systems, are considered in this paper. An approximate method is presented to assess the stationary response of multidegree, nonlinear, Markovianjump, quasinonintegrable Hamiltonian systems subjected to stochastic excitation. Using stochastic averaging, the quasinonintegrable Hamiltonian equations are first reduced to a onedimensional Itأ´ equation governing the energy envelope. The associated Fokker–Planck–Kolmogorov equation is then set up, from which approximate stationary probabilities of the original system are obtained for different jump rules. The validity of this technique is demonstrated by using a nonlinear twodegree oscillator that is stochastically driven and capable of Markovian jumps.