Stochastic three-state model with delay

We investigate here a stochastic three-state element whose transition probability depends on its state at a fixed interval in the past. A rich dynamical behavior which does not appear in a binary model is observed in this model. A resonant phenomenon due to the delay appears as well. Furthermore, an analytical expression of this resonant characteristic can be derived in general for an N-state model. We also discuss its application to the dynamical time series of yen-dollar currency exchange. (C) 2002 Elsevier Science B.V. All rights reserved.