Model Emergent Dynamics in Complex Systems

Arising from the growing interest in dynamical systems theory, this book explores the derivation of relatively simple dynamical equations that model complex physical interactions. It unifies into one coherent approach many varied extant methods for model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between multiscale models and paradoxes, and addresses model reduction for systems, resolves initial conditions, and illuminates control. The methodology focusses on the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems leading to a broad range of geometric interpretations of the modeling process that it produces. This facilitates an enhanced view of other modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, and WKB theory. Researchers at the graduate level and above who need to understand systems and modeling at different levels of resolution and complexity will find this book useful.