| We will consider the long time behavior of externally driven dynamical systems possessing several attractors. In presence of weak (Gaussian white) noise these attractors loose their stability on long time scales. Most of the time though the system will be found in the close vicinity of either of the deterministically stable states which, hence, become metastable in the presence of noise. Transitions between these metastable states are caused by the noise and occur as rare events. In this talk we will confine ourselves to periodically driven processes and discuss the form of the conditional probability density of the system for times which are large compared to the time scales of the deterministic motion. This probability density can be expressed by conditional probabilities describing the jump process between metastable states and two types of functions for each metastable state the significance of which will be discussed in more detail in the talk. A generalized flux-over-population expression for the transition rates between the metastable states will be derived. |
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