Nonstationary cyclic behavior in Markov systems Original Research Article

We introduce the concept of the nonstationary cyclic Markov system as a natural extension of the cyclic systems found in recent literature. We find the sets of d-cyclic asymptotically attainable structures and establish the relationships that exist between these structures for a nonhomogeneous Markov system in a deterministic or stochastic environment. The inherent connection between nonstationary cyclicity and stochastic environment is examined. Also we investigate the conditions under which there exists a geometric convergence to the equilibrium.