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Dynamical Systems

Dynamical systems describe the time-varying processes fundamental to many scientific theories. Classical continuous-time systems are described by ordinary or partial differential equations, whereas discrete-time systems are modeled using difference equations or cellular automata. A typical goal in dynamical systems is to predict the long term behaviour of a system as a result of perturbations or small changes to initial parameters. One of the most compelling aspects of the subject is the opportunity to study a question using a diverse set of methods such as mathematical modeling or computational and experimental investigation combined with theoretical analysis. This diversity is reflected at the Center for Applied Mathematics where faculty and students study a broad range of dynamical systems ranging from mechanical systems or fluid dynamics to questions in mathematical biology or stochastic systems in economics.