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
