This carefully edited book presents a focused debate on the mathematics and physics of chaos, nonlinearity and complexity in nature. It explores the role of non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems that draws on the relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It presents a self-contained scientific theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.
A. Sengupta (Ed.) Chaos, Nonlinearity, Complexity Studies in Fuzziness and Soft Computing, Volume 206 Editor-in-chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw Poland E-mail:
[email protected] Further volumes of this series can be found on our homepage: springer.com Vol. 190. Ying-ping Chen Extending the Scalability of Linkage Learning Genetic Algorithms, 2006 ISBN 3-540-28459-1 Vol. 191. Martin V. Butz Rule-Based Evolutionary Online Learning Systems, 2006 ISBN 3-540-25379-3 Vol. 192. Jose A. Lozano, Pedro Larrañaga, Iñaki Inza, Endika Bengoetxea (Eds.) Towards a New Evolutionary Computation, 2006 ISBN 3-540-29006-0 Vol. 193. Ingo Glöckner Fuzzy Quantifiers: A Computational Theory, 2006 ISBN 3-540-29634-4 Vol. 194. Dawn E. Holmes, Lakhmi C. Jain (Eds.) Innovations in Machine Learning, 2006 ISBN 3-540-30609-9 Vol. 195. Zongmin Ma Fuzzy Database Modeling of Imprecise and Uncertain Engineering Information, 2006 ISBN 3-540-30675-7 Vol. 196. James J. Buckley F