Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such systems? Written by international experts, Nonlinear Dynamics and Chaos: Where Do We Go from Here? assesses what the future holds for dynamics and chaos. The chapters address one or more of the broad and interconnected main themes: neural and biological systems, spatially extended systems, and experimentation in the physical sciences. The contributors offer suggestions as to what they see as the way forward, often in the form of open questions for future research.
Table of Contents
Bifurcation and Degenerate Decomposition in Multiple Time Scale Dynamical Systems
Many-Body Quantum Mechanics
Unfolding Complexity: Hereditory Dynamical Systems-New Bifurcation Schemes and High Dimensional Chaos
Uwe an der Heiden
Creating Stability out of Instability
Signal or Noise? A Nonlinear Dynamics Approach to Spatiotemporal Communication
Outstanding Problems in the Theory of Pattern Formation
Is Chaos Relevant to Fluid Mechanics?
Time-Reversed Acoustics and Chaos
Reduction Methods Applied to Nonlocally Coupled Oscillator Systems
A Prime Number of Prime Questions about Vortex Dynamics in Nonlinear Media
Spontaneous Pattern Formation in Primary Visual Cortex
Paul Bressloff and Jack Cowan
Models for Pattern Formation in Development
Spatiotemporal Nonlinear Dynamics: A New Beginning
"This handsome volume is the proceedings of a conference held in Bristol in 2001, which had the aim of charting new directions for the exploration of nonlinear dynamical systems. The editors must be commended for their work: the individual chapters have been given a clean, uniform style that reflects a serious effort to present the volume as a unified book rather than a recollection of articles, with several cross-references between the chapters. The book is also remarkably free of typographical errors. I heartily recommend this collection to students looking for some direction (as long as they don't think this is all of nonlinear dynamics!)."
-UK Nonlinear News, May 2003
"This timely and important book is a record of papers presented at a conference in Bristol and is very well edited, and produced … The very richness of this book, in both theory and real-world applications, makes it difficult to summarize and even more difficult to put down."
-Nonlinear Dynamics, Psychology and Life Sciences
"The book is written by authors who are champions of their field. All researchers in nonlinear dynamics should have access to this book. It is a valuable resource of references and it contains a lot of ideas and open problems in various fields. One might think of it as a catalogue of problems in nonlinear dynamics. The introduction of the book is a 'must-read.' It presents the nature and the philosophy of the book (and the symposium). Reading the introduction, the editors clearly have done a great job of managing each of the invited lecturers to translate the philosophy of the symposium into their lectures … my impression is that all authors did a good job presenting the excitement of their research and addressing the interesting questions. This book in general is a valuable addition to the literature of the theory and practice of nonlinear dynamics and chaos."
-Theo Tuwankotta, Institute of Technology,ITB, Bandung, Indonesia