A new edition of this well-established monograph, this volume provides a comprehensive overview over the still fascinating field of chaos research. The authors include recent developments such as systems with restricted degrees of freedom but put also a strong emphasis on the mathematical foundations. Partly illustrated in color, this fourth edition features new sections from applied nonlinear science, like control of chaos, synchronisation of nonlinear systems, and turbulence, as well as recent theoretical concepts like strange nonchaotic attractors, on-off intermittency and spatio-temporal chaotic motion.

Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com plex nonlinear systems that cannot be broken down into the behavior of their con stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many are often highly idealized or time independent.

In economics agents are assumed to choose on the basis of rational calculations aimed at the maximization of their pleasure or profit. Formally, agents are said to manifest transitive and consistent preferences in attempting to maximize their utility in the presence of several constraints. They operate according to the choice imperative: given a set of alternatives, choose the best. This imperative works well in a static and simplistic framework, but it may fail or vary when 'the best' is changing continuously. This approach has been questioned by a descriptive approach that springing from the complexity theory tries to give a scientific basis to the way in which individuals really choose, showing that those models of human nature is routinely falsified by experiments since people are neither selfish nor rational. Thus inductive rules of thumb are usually implemented in order to make decisions in the presence of incomplete and heterogeneous information sets.

Aims to reinforce the interface between physical sciences, theoretical computer science, and discrete mathematics. This book assembles theoretical physicists and specialists of theoretical informatics and discrete mathematics in order to learn about developments in cryptography, algorithmics, and more.

This book contains the Proceedings of the 2007 Conference of the Italian Systems Society. Papers deal with the interdisciplinary study of processes of emergence, considering theoretical aspects and applications from physics, cognitive science, biology, artificial intelligence, economics, architecture, philosophy, music and social systems. Such an interdisciplinary study implies the need to model and distinguish, in different disciplinary contexts, the establishment of structures, systems and systemic properties. Systems, as modeled by the observer, not only possess properties, but are also able to make emergent new properties. While current disciplinary models of emergence are based on theories of phase transitions, bifurcations, dissipative structures, multiple systems and organization, the present volume focuses on both generalizing those disciplinary models and identifying correspondences and new more general approaches. The general conceptual framework of the book relates to the attempt to build a general theory of emergence as a general theory of change, corresponding to Von Bertalanffy''s project for a general system theory.

In this book the authors consider the natural environment as an integrated system. The physical, chemical and biological processes that govern the behaviour of the environmental system can thus be understood through mathematical modelling, and their evolution can be studied by means of numerical simulation. The book contains a summary of various efficient approaches in atmospheric prediction, such as numerical weather prediction and statistical forecast of climate change, as well as other successful methods in land surface modelling. The authors explore new theories and methods in environment prediction such as systems analysis and information theory. Attention is given to new achievements in remote sensing tele-metering and geographic information systems.