Dynamical systems, stability, & chaos

In this project we will review aspects of the mathematics of dynamical systems, stability, and chaos within a historical framework that draws together the two major threads of its early development: celestial mechanics and control theory, and focusing on qualitative theory. From this perspective we will study how concepts of stability enable us to classify dynamical equations and their solutions and connect the key issues of nonlinearity, bifurcation, control, and uncertainty that are common to time-dependent problems in natural and engineered systems. Building on this foundation, we may investigate new problems involving stability of large complex networks, such as transport, communications, or ecological networks.