Information Dynamics Foundations and Applications [Paperback]

This book offers a new, theoretical approach to information dynamics, i.e., information processing in complex dynamical systems. The presentation establishes a consistent theoretical framework for the problem of discovering knowledge behind empirical, dynamical data and addresses applications in information processing and coding in dynamical systems. This will be an essential reference for those in neural computing, information theory, nonlinear dynamics and complex systems modeling.This book originated from a forefront R&D project pursued at Siemens Corporate Technology over the past several years. As a name for this project, we chose Information Dynamics , which stands for information processing in complex dynamical systems. In the project, we wanted to grasp the flow of information in such systems in a quantitative manner, on the one hand by making use of an existing arsenal of methods and techniques from areas such as information theory, mathematical statistics, neural networks, nonlinear dynamics, probability theory, and statistical physics, and on the other hand by deriving new methods and techniques if required. The book contains only those contributions to the above-mentioned project which lend themselves to a unifying theoretical framework. Other important results obtained in the project, such as the extension of transport-theoretic techniques and their application to optimizing traffic flow, or the design of new neural network architectures for treating systems at the edge of chaos with applications in economics, are left out. This certainly is a sacrifice, but we think it is of benefit to the reader that we tried to be as focused and self? contained as possible.l Introduction.- 2 Dynamical Systems: An Overview 7.- 2.1 Deterministic Dynamical Systems.- 2.1.1 Fundamental Concepts.- 2.1.2 Attractors.- 2.1.3 Strange Attractors: Chaotic Dynamics.- 2.1.4 Quantitative Description of Chaos.- 2.1.5 Chaotic Dynamical Systems.- 2.2 Stochastic Dynamical Systems.ló$