Dynamical Systems Theory

Catalog description

Complex dynamics are not only ubiquitous but increasingly evident in the highly interconnected modern world. From the global scale of ecological and social systems to the molecular scale of gene regulation, complexity emerges in evolving network architectures. This course introduces the concepts and computational techniques of dynamical systems theory, with a focus on complexity science--the study of systems characterized by a large number of interacting components and adaptive interactions. Reviews the basic principles of graph and network theory before exploring fundamental concepts of dynamical systems theory, including continuous and discrete systems, differential and difference equations, attractor dynamics, bifurcation and chaos. Students become familiar with several computational techniques through the analysis of concrete examples of both deterministic and stochastic dynamics, as well as powerful visualization strategies for effectively communicating their results. Concludes with an overview of machine learning techniques relevant to analyzing the dynamics of complex systems.