Complexity Explorer Santa Fe Institute

Course Syllabus

Complexity and Chaos in Dynamical Systems

The module aims to introduce some of the techniques used in the modern theory of dynamical systems and the concepts of chaos and strange attractors, and to illustrate a range of applications to problems in the physical, biological and engineering sciences. Dynamical systems are represented by mathematical models that describe different phenomena whose state (or instantaneous description) changes over time. Examples are mechanics in physics, population dynamics in biology and chemical kinetics in chemistry. One basic goal of the mathematical theory of dynamical systems is to determine or characterise the long-term behaviour of the system using methods for analysing differential equations and iterated mappings. Interestingly, simple deterministic nonlinear dynamical systems and even piecewise linear systems can exhibit a completely unpredictable behaviour, which might seem to be random. This behaviour of systems is known as deterministic chaos.

University of Warwick
Dr Yulia Timofeeva
Chaos, Dynamical Systems