Description

Many phenomena are thought to be deterministic (that is, one can predict their future states by knowing their present states). What happens if one can measure state variables only with a given tolerance? Do two nearby present states of a given deterministic system always lead to nearby fates?

Computer experiments by Edward Norton Lorenz in the 1960s revealed a striking feature of non-linear deterministic processes. Namely, Lorenz observed that a particular system can take extremely close initial states to diverse future states. Thus giving a decisive "no" to the question raised above, and providing a particular deterministic system with so-called 'sensitivity to initial conditions' which is a key feature of chaos in the mathematical sense. Here is a video using the system that Lorenz used in his experiments.

The goal of the project is to find order and generating mechanisms in chaotic systems.

Pre-/Co-requisites

Resources

• Morris W. Hirsch, Stephen Smale, Robert L. Devaney. 2004: Differential equations, dynamical systems, and an introduction to chaos
• Stephen Wiggins: Introduction to applied nonlinear dynamical systems and chaos