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)
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.