Discrete Dynamical Systems: Theory and Applications

This textbook is an elementary introduction to the world of dynamical systems and chaos. Dynamical systems provide a mathematical means of modelling and analyzing aspects of the changing world around us. The aim of this text is to introduce the reader both to the wide variety of techniques used to study dynamical systems and to their many applications. In particular, investigation of dynamical systems leads to the important concepts of stability, strange attractors, chaos and fractals. An important theme of the book is to show students that some dynamical systems have stable solutions whereas others may exhibit seemingly chaotic patterns of behaviour. Amongst the many real-world applications studied in this book are the growth of compound interest, population growth, the dilution of drugs in the body, and problems in genetics. Very little previous mathematical knowledge is assumed: an elementary exposure to calculus and linear algebra would be sufficient for a student to enjoy and benefit from this text. The author illustrates the theory with a large supply of worked examples and numerous exercises of varying degrees of difficulty. Throughout students are encouraged to experiment with models of dynamical systems on computers and explore for themselves this area of mathematics.