Overview

This collection of articles introduces the idea of a hierarchical order in chaotic systems and natural phenomena. To understand nature, nonlinear sciences use a multidisciplinary perspective. Therefore the book integrates research work of different fields: experimental evidence for the theory drawn from physics, biology and chemistry; theoretical progress in mathematical treatment, numerical techniques and graphical methods of nonlinear sciences; and to not-yet-understood philosophical and fundamental problems related to chaos and cosmos, chaos and quantum mechanics or evolutionary dynamics. Featuring the most recent advances in nonlinear dynamics this collection should provide an indispensable reference source and starting point for further research concerning dynamical and hierarchical chaotic systems. Besides this book is in honor of Professor O E Rössler, one of the pioneers of Chaos Theory, who celebrated his 50th birthday in May 1990.Contents: Hierarchies of Dynamical Systems (M Klein & G Baier) The Chaotic Hierarchy (O E Rössler) Phase Regulation of Coupled Oscillators and Chaos (R H Abraham) Symbolic Dynamics in the Belousov-Zhabotinskii Reaction: From Rössler's Intuition to Experimental Evidence for Shil'nikov's Homoclinic Chaos (F Argoul et al.) Determinism in a World of Non-Invertible Transformations (H Degn) Structural, Functional and Dynamical Hierarchies in Neural Networks (A V Holden) Climbing Up Dynamical Hierarchy (K Kaneko) Chaotic Hierarchy from the One-Dimensional Box-Within-a-Box Bifurcations Structure Properties (Ch Mira) The Peroxidase-Oxidase Reaction: A Case for Chaos in the Biochemistry of the Cell (L F Olsen et al.) Experimental Progress on the Ladder Towards Higher Chaos (J Peinke et al.) Conjugate Pair of Representations in Chaos and Quantum Mechanics (K Tomita) Readership: Mathematicians, mathematical physicists and condensed matter physicists.

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