Stochastic dynamics in models sensitive to noise

Many systems which are sensitive to noise exhibit dynamical features from both the underlying deterministic behavior and the stochastic elements. Then the stochastic effects are obscured in this mix of dynamics. Several different methods have recently been applied to separate the "deterministic" and "stochastic" dynamics. These approaches lead to simplified approximate models which can be analyzed or simulated efficiently, providing useful measures of the noise sensitivity. The methods combine projection methods and the identification of important scaling relationships to exploit features common to these systems, such as the presence of multiple time scales, limited regions of strong noise-sensitivity, and resonances. These approaches are valuable for studying a variety of problems, including stochastic delay-differential equations, noisy bursters, and meta-stable interfaces. The approach will be outlined in one or two of these applications, and the generalization to other areas will be discussed. The results have interesting connections to classical probabilistic methods, dynamical systems analysis, and singular perturbation theory.