- About this module
- Learning objectives
- Prerequisites
- Module map
- Assessment
- Book list

### About This Module.

This module has been written by | Pam Valks
| Chris Bloor
| Doug Curran
| Walter Middleton

At Sunderland University.

### Learning objectives

In a dynamical system the model, usually a set of differential or differenceequations, determines the evolution of the system given only its initialstate i.e. the long term behaviour is known once the initial conditionsare known. The aim of this module is to learn how to use a model to predictthe long term behaviour of a system by analytical and qualitative methods.You will learn

- To investigate the stability of a system.
- To understand the importance of initial conditions and understand the meaningof the terms attractor and repellor.
- 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 systems to initial conditions.

### Prerequisites

It is recommended that you have some knowledge of the following topics.

- Algebra.
General manipulative skills including inequalities. Solution of simultaneous,quadratic and cubic equations. Theory of quadratic and cubic equations
- Functions.
Knowledge of polynomial, trigonometric, exponential, logarithmic andhyperbolic functions.
- Calculus.
Concept of derivative as a gradient. Differentiation of polynomials,trigonometric, exponential, logarithmic and hyperbolic functions. Conceptof partial derivatives. Concept of integration and the evaluation of integrals.Solution of simple differential equations.

These topics are covered by the module Computor Based Mathematics 1at Sunderland University.

### Module Map.

This dynamical systems module consists of five units each of which is subdividedinto sections as shown in the diagram below. The module should take approximately150hrs of study time.

### Assessment

### Book list

- Arrowsmith and Place Dynamical Systems
- Barnsley M.F. Fractals Everywhere
- Berry J. Introduction To Nonlinear Systems
- Blanchland,Devaney and Hall Differential Equations
- Kaplan D. and Glass L. Understanding Nonlnear Dynamics.
- Gleick J. Chaos-The making of a New Science
- Guterman and Nilecki Differential Equations -A First Course
- Mandlebrot The Fractal Geometry Of Nature
- Peitgen, J rgus and Saupe Fractals For The Classroom
- Strogatz S.M. Nonlinear Dynamics And Chaos