Coordination: Neural, Behavioral and Social Dynamics

Springer Science & Business Media
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One of the most striking features of Coordination Dynamics is its interdisciplinary character. The problems we are trying to solve in this field range from behavioral phenomena of interlimb coordination and coordination between stimuli and movements (perception-action tasks) through neural activation patterns that can be observed during these tasks to clinical applications and social behavior. It is not surprising that close collaboration among scientists from different fields as psychology, kinesiology, neurology and even physics are imperative to deal with the enormous difficulties we are facing when we try to understand a system as complex as the human brain.

The chapters in this volume are not simply write-ups of the lectures given by the experts at the meeting but are written in a way that they give sufficient introductory information to be comprehensible and useful for all interested scientists and students.

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Springer Science & Business Media
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Published on
Dec 11, 2007
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Mathematics / Applied
Mathematics / Linear & Nonlinear Programming
Mathematics / Mathematical Analysis
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Science / Mechanics / Dynamics
Science / Physics / General
Science / Physics / Mathematical & Computational
Technology & Engineering / Manufacturing
Technology & Engineering / Mechanical
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The past two decades have witnessed an explosion of ideas in the general ?eld of nonlinear dynamics. In fact, it has become increasingly clear that areas as diverse as signal processing, lasers, molecular motors, and biomedical anomalies have a c- mon underlying thread: the dynamics that underpin these systems are inh- ently nonlinear. Yet, while there has been signi?cant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions andpreparations,thereexistcomparativelyfewdevicesthatactuallytakethis rich behavior into account. In the presence of background noise (a given, for most practical appli- tions), the underlying dynamic phenomena become even richer, with the noise actually mediating cooperative behavior that, when properly understood, can lead to signi?cant performance enhancements; a striking example of this - havior occurs, for example, when the underlying dynamics undergoes a bif- cation from static to oscillating behavior when a control parameter is swept through a critical value. If properly understood, theoretically, the (suitably quanti?ed) system response can be signi?cantly enhanced near the onset of the bifurcation. Examples of this behavior have been observed in a large n- ber of laboratory experiments on systems ranging from solid state lasers, to SQUIDs, and such behavior has been hypothesized to account for some of the more striking information processing properties of biological neurons. In many cases, background noise can precipitate this behavior, thereby playing a signi?cant role in the optimization of the response of these systems to small external perturbations.
'Vibrations and Stability' is aimed at third to fifth-year undergraduates and post graduates in mechanical or structural engineering. The book covers a range of subjects relevant for a one-or two-semester course in advanced vibrations and stability. Also, it can be used for self-study, e. g. , by students on master or PhD projects, researchers, and professional engineers. The focus is on nonlinear phe nomena and tools, covering the themes of local perturbation analysis (Chaps. 3 and 4), bifurcation analysis (Chap. 5), global analysis I chaos theory (Chap. 6), and special high-frequency effects (Chap. 7). The ground for nonlinear analysis is laid with a brief summary of elementary linear vibration theory (Chap. 1), and a treatment of differential eigenvalue problems in some depth (Chap. 2). Also, there are exercise problems and extensive bibliographic references to serve the needs of both students and more experienced users; major exercises for course-work; and appendices on numerical simulation, standard mathematical formulas, vibration properties of basic structural elements, and properties of engineering materials. This Second Edition is a revised and expanded version of the first edition (pub lished by McGraw-Hill in 1997), reflecting the experience gathered during its now six years in service as a classroom or self-study text for students and researchers. The second edition contains a major new chapter (7), three new appendices, many new exercise problems, more than 120 new and updated bibliographic references, and hundreds of minor updates, corrections, and clarifications.
With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified.

This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work.

“This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future.”

“With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems.”

“What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically.”

(J.A.Scott Kelso, excerpts from the foreword)

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