Chaos is typically understood as a mathematical property of a dynamical system. A dynamical system can be considered to be a model that evolves through time, where time is either continuous or discrete. Together with chaos theory they explore the evolution of qualitative behaviour. Examples of dynamical systems include the weather or even the number of cars going through a junction.
We will look at investigating non-linear dynamical systems that are defined at discrete times. A discrete-time system uses current states as input and generates new states as output. Moreover, we will be exploring questions such as why chaotic behaviour arises. We will focus on looking at sensitivity to initial conditions, and, explore the different ways to represent the behaviour of dynamical systems.
Two maps that we will be looking at are the quadratic map (logistic map) and the tent map, both of which are the simplest examples of how models illustrate chaotic behaviour.