The interplay between synchronization and spatio-temporal pattern formation is central for a broad variety of phenomena in nature, such as the coordinated contraction of heart tissue, associative memory and learning in neural networks, and pathological synchronization during Parkinson disease or epilepsy. In this thesis, three open puzzles of fundametal research in Nonlinear Dynamics are tackled: How does spatial confinement affect the dynamics of three-dimensional vortex rings? What role do permutation symmetries play in the spreading of excitation waves on networks? Does the spiral wave chimera state really exist? All investigations combine a theoretical approach and experimental verification, which exploit an oscillatory chemical reaction. A novel experimental setup is developed that allows for studying networks with N > 1000 neuromorphic relaxation oscillators. It facilitates the free choice of network topology, coupling function as well as its strength, range and time delay, which can even be chosen as time-dependent. These experimental capabilities open the door to a broad range of future experimental inquiries into pattern formation and synchronization on large networks, which were previously out of reach.

TIlis volume contains the contributions to the Euromech Colloquium No. 241 on Nonlinear Waves in Active Media at the Institute of Cybernetics of the Estonian Academy of Sciences, Tallinn, Estonia, USSR, September 27-30, 1988. The Co-chairmen of the Euromech Colloquium felt that it would be a good service to the community to publish these proceedings. First, the topic itself dealing with various wave processes with energy influx is extremely interesting and attracted a much larger number of participants than usual - a clear sign of its importance to the scientific community. Second, Euromech No. 241 was actually the first Euromech Colloquium held in the Soviet Union and could thus be viewed as a milestone in the extending scientific contacts between East and West. At the colloquium 50 researchers working in very different branches of sci ence met to lecture on their results and to discuss problems of common interest. An introductory paper by I. Engelbrecht presents the common motivation and background of the topics covered. Altogether 36 speakers presented their lectures, of which 30 are gathered here. The remaining six papers which will appear elsewhere are listed on page X. In addition, three contributions by authors who could not attend the colloquium are included. The two lectures given by A.S. Mikhailov, V.S. Davydov and V.S. Zykov are here published as one long paper.

According to its definition, Synergetics is concerned with systems that produce macroscopic spatial, temporal, or functional structures. Autowaves are·a specific, yet very important, case of spatio-temporal structures. The term "autowave" was coined in the Soviet Union in analogy to the term "auto-oscillator". This is - perhaps too literal - translation of the Russian word "avto-ostsillyatory" (= self oscillator) which in its proper translation means "self-sustained oscillator". These are oscillators, e. g. , clocks, whose internal energy dissipation is compensa ted by a (more or less) continuous power input. Simi larly, the term "autowaves" de notes propagation effects - including waves - in active media, which provide spa tially distributed energy sources and thus may compensate dissipation. An example which is now famous is represented by spiral or concentric waves in a chemically active medium, undergoing the Belousov-Zhabotinsky reaction. This book provides the reader with numerous further examples from physics, chem istry, and biology - e. g. , autowaves of the heart. While the Belousov-Zhabotinsky reaction is now widely known, a number of very important results obtained in the Soviet Union are perhaps less well known. I am particularly glad that this book may help to make readers outside the Soviet Union acquainted with these important exper imental and theoretical findings which are presented in a way which elucidates the common principles underlying this kind of propagation effects. Professor V.

Wavelet analysis and its applications have been one of the fastest growing research areas in the past several years. Wavelet theory has been employed in numerous fields and applications, such as signal and image processing, communication systems, biomedical imaging, radar, air acoustics, and many other areas. Active media technology is concerned with the development of autonomous computational or physical entities capable of perceiving, reasoning, adapting, learning, cooperating, and delegating in a dynamic environment.This book captures the essence of the current state of the art in wavelet analysis and active media technology. It includes nine invited papers by distinguished researchers: P Zhang, T D Bui and C Y Suen from Concordia University, Canada; N A Strelkov and V L Dol'nikov from Yaroslavl State University, Russia; Chin-Chen Chang and Ching-Yun Chang from Taiwan; S S Pandey from R D University, India; and I L Bloshanskii from Moscow State Regional University, Russia.The proceedings have been selected for coverage in:

Wavelet analysis and its applications have been one of the fastest-growing research areas in the past several years. Wavelet theory has been employed in numerous fields and applications, such as signal and image processing, communication systems, biomedical imaging, radar, and air acoustics. Active media technology is concerned with the development of autonomous computational or physical entities capable of perceiving, reasoning, adapting, learning, cooperating, and delegating in a dynamic environment.This book captures the essence of the state of the art in wavelet analysis and its applications and active media technology. At the Congress, invited talks were delivered by distinguished researchers, namely Prof John Daugman of Cambridge University, UK; Prof Bruno Torresani of INRIA, France; Prof Victor Wickerhauser of Washington University, USA, Prof Ning Zhong of the Maebashi Institute of Technology, Japan; Prof John Yen of Pennsylvania State University, USA; and Prof Sankar K Pal of the Indian Statistical Institute, India.

Wavelet analysis and its applications have been one of the fastest-growing research areas in the past several years. Wavelet theory has been employed in numerous fields and applications, such as signal and image processing, communication systems, biomedical imaging, radar, and air acoustics. Active media technology is concerned with the development of autonomous computational or physical entities capable of perceiving, reasoning, adapting, learning, cooperating, and delegating in a dynamic environment.This book captures the essence of the state of the art in wavelet analysis and its applications and active media technology. At the Congress, invited talks were delivered by distinguished researchers, namely Prof John Daugman of Cambridge University, UK; Prof Bruno Torresani of INRIA, France; Prof Victor Wickerhauser of Washington University, USA, Prof Ning Zhong of the Maebashi Institute of Technology, Japan; Prof John Yen of Pennsylvania State University, USA; and Prof Sankar K Pal of the Indian Statistical Institute, India.

This book contains review papers presented at the International Workshop on Wave Propagation, Scattering and Emission on Theory, Experiment, Simulation and Inversion (WPSE). The papers are of high quality, covering broad areas: a new mechanism of interaction of electromagnetic waves with complex media, remote sensing information, computational electromagnetics, etc. This book summarizes the most significant progress in wave propagation, encompassing theory, experiment, simulation, and inversion. It will also serve as a good reference for scientists in future research.List of Foreign Invited Speakers: Henry Bertoni (Brooklyn Polytechnic University), Lawrence Carin (Duke U), Al Chang (NASA, Goddard), Margaret Cheney (Rensselaer Polytech Institute), Weng Chew (U of Illinois at Urbana Champaign), Shane Cloude (AEL Consultants, UK), Adrian Fung (U of Texas at Arlington), Al Gasiewski (Environmental Tech Lab, NOAA), Martti Hallikainen (Helsinki U of Technology), Akira Ishimaru (U of Washington), Magdy Iskander (U of Hawaii), J A Kong (MIT), Roger Lang (George Washington U), Alex Maradudin (U of California at Irvine), Eric Michielssen (U of Illinois at Urbana Champaign), Eni Njoku (Caltech, Jet Propulsion Lab), Carey Rappaport (Northeastern U), Marc Saillard (Institut Fresnel), Kamal Sarabandi (U of Michigan), David R Smith (U of California at San Diego), Mitsuo Tateiba (Kyushu University), George Uslenghi (U of Illinois at Chicago), and Werner Wiesbeck (Karlsruhe U).

This book develops analytical methods for studying the dynamical chaos, synchronization, and dynamics of structures in various models of coupled rotators. Rotators and their systems are defined in a cylindrical phase space, and, unlike oscillators, which are defined in Rn, they have a wider “range” of motion: There are vibrational and rotational types for cyclic variables, as well as their combinations (rotational-vibrational) if the number of cyclic variables is more than one. The specificity of rotator phase space poses serious challenges in terms of selecting methods for studying the dynamics of related systems. The book chiefly focuses on developing a modified form of the method of averaging, which can be used to study the dynamics of rotators. In general, the book uses the “language” of the qualitative theory of differential equations, point mappings, and the theory of bifurcations, which helps authors to obtain new results on dynamical chaos in systems with few degrees of freedom. In addition, a special section is devoted to the study and classification of dynamic structures that can occur in systems with a large number of interconnected objects, i.e. in lattices of rotators and/or oscillators. Given its scope and format, the book can be used both in lectures and courses on nonlinear dynamics, and in specialized courses on the development and operation of relevant systems that can be represented by a large number of various practical systems: interconnected grids of various mechanical systems, various types of networks including not only mechanical but also biological systems, etc.