## Center for Applied Mathematics Colloquium

Studying computational simulations as dynamical systems have many scientific engineering applications. In this talk, we investigate how a chaotic dynamical system responds to small perturbations. When the dynamical system is a computational simulation, these perturbations can be design changes, environmental noise, numerical error, and modeling uncertainties. We show that many classic concepts and methods for sensitivity and stability analysis do not apply to long time averaged quantities of interest in the presence of chaos. We introduce concepts and techniques applicable to chaotic flows, including Lyapunov spectrum analysis and least squares shadowing method. We demonstrate applications of these concepts and technology and illustrate remaining open questions.