# INTRODUCTION

In a dynamical system the model, usually a set of differential ordifference equations determines the evolution of the system given onlyits initial state i.e. the long term behaviour is known once the initialconditions are known. The aim of this module is to learn how to use a modelto predict the long term behaviour of a system by analytical and qualitativemethods. You will learn

- To investigate the stability of a system and understand the meaning ofthe terms attractor and repellor
- To understand the importance of initial conditions
- To understand the significance of the values of the parameters in a model
- To describe qualitatively the long term behaviour of a system
- To understand the sensitivity of chaotic sysems on inital conditions

### References.

You will find a list of useful references by clicking on the iconat the top right hand side of the screen. Try it now so that you can becomefamiliar with the contents.

When you are using the reference window if you click outside the windowit will disappear from your screen. To return the window click on "reference"onthe view bar at the bottom (or top ) of your screen.

If you click on the icon and nothing happens it is probably becauseyou already have a reference window open which is hidden. Click on "reference" on the view bar to return the window to your screen.

### Maple.

You will find a list of useful Maple worksheets by clicking on the icon at the top right hand side of the screen. Clicking on the worksheet title will openthe worksheet in a Maple window.

Like this worked example