Mathematicians have been aware of chaotic dynamics since Poincaré’s work at the turn of the century. But, as the turn of yet another century approaches, physical scientists and engineers have begun to use their understanding of chaos theory to analyze chaotic experimental time series data. Some researchers have even used the presence of chaos to achieve practical goals. To do this, they have had to work with dynamical processes for which the equations were either not known or were too complex to be useful. In other words, they have been coping with chaos.
Coping With Chaos is the first book to bring together recent advances in the interpretive and practical applications of chaos, which hold great promise for broad applicability throughout the physical sciences and engineering. Together with an introduction to chaos theory, this book provides detailed reports on methods of analyzing experimental time series data from chaotic systems and studies in which the unique attributes of chaos are put to practical use. Topics discussed in this book include:
• Theory of chaotic dynamics
• Embedding techniques for the analysis of experimental data
• Calculation of dimension and Lyapunov exponents
• Determination of periodic orbits and symbolic dynamics
• Prediction of chaotic time series
• Noise filtering of chaotic data
• Control of chaotic systems
• The use of Chaotic signals for communication
• And more
Spanning the wide reach of nonlinear dynamics throughout mathematics and natural and physical science, Chaos: An Introduction To Dynamical Systems develops and explains the most intriguing and fundamental elements of the topic, and examines their broad implications.
Among the major topics included are discrete dynamical systems, chaos, fractals, nonlinear differential equations, and bifurcations. The text also features Lab Visits, short reports that illustrate relevant concepts from the physical, chemical, and biological sciences, drawn from the scientific literature. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulation, designed to be used with any standard software package. And each chapter ends with a Challenge, which provides students with a tour through an advanced topic in the form of an extended exercise.