Nonlinear Phenomena Research Perspectives

Non-linear, or chaotic behaviour in real world systems has been reported in electronic circuits and communications systems, chemical reactions, biological behaviour. Applications include solitons, integrable systems, cellular automata, pattern formation, qualitative structure and bifurcation theory, onset of chaos and turbulence, analytic dynamics, and transport phenomena. This book presents important new research in this dynamic field.

The Advanced Study Institute (ASI) on Nonlinear Phenomena-in Physics and Biology was held at the Banff Centre, Banff, Alberta, Canada, from 17 - 29 August, 1980. The Institute was made possible through funding by the North Atlantic Treaty Organization (who sup plied the major portion of the financial aid), the National Research and Engineering Council of Canada, and Simon Fraser University. The availability of the Banff Centre was made possible through the co sponsorship (with NATO) of the ASI by the Canadian Association of Physicists. 12 invited lecturers and 82 other participants attended the Institute. Except for two lectures on nonlinear waves by Norman Zabusky, which were omitted because it was felt that they already had been exhaustively treated in the available literature, this volume contains the entire text of the invited lectures. In addition, short reports on some of the contributed talks have also been included. The rationale for the ASI and this resulting volume was that many of the hardest problems and most interesting phenomena being studied by scientists today ar.e nonlinear in nature. The nonlinear models involved often span several different disciplines, °a simple example being the Volterra-type model in population dynamics which has its analogue in nonlinear optics and plasma physics (the 3-wave problem), in the discussion of the social behavior of animals, and in biological competition and selection at the molecular level.

The study of dark matter, in both astrophysics and particle physics, has emerged as one of the most active and exciting topics of research in recent years. This book reviews the history behind the discovery of missing mass (or unseen mass) in the Universe, and ties this into the proposed extensions to the Standard Model of Particle Physics (such as Supersymmetry), which were being proposed within the same time frame. This book is written as an introduction to these problems at the forefront of astrophysics and particle physics, with the goal of conveying the physics of dark matter to beginning undergraduate majors in scientific fields. The book goes onto describe existing and upcoming experiments and techniques, which will be used to detect dark matter either directly on indirectly.

Increasing interest in the study of coordinated activity of brain cell ensembles reflects the current conceptualization of brain information processing and cognition. It is thought that cognitive processes involve not only serial stages of sensory signal processing, but also massive parallel information processing circuitries, and therefore it is the coordinated activity of neuronal networks of brains that give rise to cognition and consciousness in general. While the concepts and techniques to measure synchronization are relatively well characterized and developed in the mathematics and physics community, the measurement of coordinated activity derived from brain signals is not a trivial task, and is currently a subject of debate. Coordinated Activity in the Brain: Measurements and Relevance to Brain Function and Behavior addresses conceptual and methodological limitations, as well as advantages, in the assessment of cellular coordinated activity from neurophysiological recordings. The book offers a broad overview of the field for investigators working in a variety of disciplines (neuroscience, biophysics, mathematics, physics, neurology, neurosurgery, psychology, biomedical engineering, computer science/computational biology), and introduces future trends for understanding brain activity and its relation to cognition and pathologies. This work will be valuable to professional investigators and clinicians, graduate and post-graduate students in related fields of neuroscience and biophysics, and to anyone interested in signal analysis techniques for studying brain function.

Since the early 1990s, when synchronization of chaotic communication systems became a popular research subject, a vast number of scientific papers have been published. However, most of today’s books on chaotic communication systems deal exclusively with the systems where perfect synchronization is assumed, an assumption which separates theoretical from practical, real world, systems. This book is the first of its kind dealing exclusively with the synchronization techniques for chaotic communication systems. It describes a number of novel robust synchronization techniques, which there is a lack of, for single and multi-user chaotic communication systems published and highly cited in world’s leading journals in the area. In particular, it presents a solution to the problem of robust chaotic synchronization by presenting the first fully synchronized, highly secure, chaos based DS-CDMA system. The book fills a gap in the existing literature where a number of books exist that deal with chaos and chaotic communications but not with synchronization of chaotic communication systems. It also acts as a bridge between communication system theory and chaotic synchronization by carefully explaining the two concepts and demonstrating how they link into chaotic communication systems. The book also presents a detailed literature review on the topic of synchronization of chaotic communication systems. Furthermore, it presents the literature review on the general topic of chaotic synchronization and how those ideas led to the application of chaotic signals to secure chaotic communication systems. It therefore, in addition to presenting the state of the art systems, also presents a detailed history of chaotic communication systems. In summary, the book stands out in the field of synchronization techniques for chaotic communication systems.

This volume covers recent advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological methods. A broad range of topics is covered, including: * concentration phenomena in pdes * variational methods with applications to pdes and physics * periodic solutions of odes * computational aspects in topological methods * mathematical models in biology Though well-differentiated, the topics covered are unified through a common perspective and approach. Unique to the work are several chapters on computational aspects and applications to biology, not usually found with such basic studies on pdes and odes. The volume is an excellent reference text for researchers and graduate students in the above mentioned fields. Contributors: M. Clapp, M. Del Pino, M.J. Esteban, P. Felmer, A. Ioffe, W. Marzantowicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, E. Séré, E. Schwartzman, P. Sintzoff, R. Turner , M. Willem.

This book is a comprehensive overview of the main current concepts in brain cognitive activities at the global, collective (or network) level, with a focus on transitions between normal neurophysiology and brain pathological states. It provides a unique approach of linking molecular and cellular aspects of normal and pathological brain functioning with their corresponding network, collective and dynamical manifestations that are subsequently extended to behavioral manifestations of healthy and diseased brains. This book introduces a high-level perspective, searching for simplification amongst the structural and functional complexity of nervous systems by consideration of the distributed interactions that underlie the collective behavior of the system. The authors hope that this approach could promote a global comprehensive understanding of high-level laws behind the elementary biological processes in the neuroscientific community, while, perhaps, introducing elements of biological complexities to the mathematical/computational readership. The title of the book refers to the main point of the monograph: that there is a smooth continuum between distinct brain activities resulting in different behaviors, and that, due to the plastic nature of the brain, the behavior can also alter the brain function, thus rendering artificial the boundaries between the brain and its behavior.

Nonlinear Physics of Ecosystems introduces the concepts and tools of pattern formation theory and demonstrates their utility in ecological research using problems from spatial ecology. Written in language understandable to both physicists and ecologists in most parts, the book reveals the mechanisms of pattern formation and pattern dynamics. It also explores the implications of these mechanisms in important ecological problems. The first part of the book gives an overview of pattern formation and spatial ecology, showing how these disparate research fields are strongly related to one another. The next part presents an advanced account of pattern formation theory. The final part describes applications of pattern formation theory to ecological problems, including self-organized vegetation patchiness, desertification, and biodiversity in changing environments. Focusing on the emerging interface between spatial ecology and pattern formation, this book shows how pattern formation methods address a variety of ecological problems using water-limited ecosystems as a case study. Readers with basic knowledge of linear algebra and ordinary differential equations will develop a general understanding of pattern formation theory while more advanced readers who are familiar with partial differential equations will appreciate the descriptions of analytical tools used to study pattern formation and dynamics.