Discrete Dynamical Systems and Chaos

This book brings to undergraduate level some of the fundamental ideas, definitions, and results on dynamical systems and chaos. This largely new and interdisciplinary field of study is necessary for understanding the frequently unexpected behaviour of many dynamical processes of great interest to physics, chemistry, biology, engineering, medicine, economics, etc. Weather patterns, laser pulsations, chemical reactions, cardiac arrythmias, epilepsy, neural networks processes, market prices and oscillations are some of the areas where the presence of chaotic behaviour has been detected. In the book, definitions, results, and examples of dynamical systems, either chaotic or not, are carefully adjusted to the proper level, to give an undergraduate, particularly a science major, a solid and informative introduction to this new field of knowledge. Primary emphasis is given to the mathematical aspects of the theory, but importyant ideas and applications proposed and developed by engineers, meterologists, biologists etc, play a considerable role throughout. Four dynamical systems derived from the current research literature are analyzed in the last chapter using the ideas and tecyhniques presented in the book. Among them, the reader will find the system proposed by E N Lorenze to model atmospheric changes and the neural network model developed by J J Hopfield.