Complex Dynamics and Morphogenesis: An Introduction to Nonlinear Science

✍ Scribed by Chaouqi Misbah (auth.)

• Publisher: Springer Netherlands
• Year: 2017
• Tongue: English
• Leaves: 475
• Edition: 1
• Category: Library

✦ Synopsis

This book offers an introduction to the physics of nonlinear phenomena through two complementary approaches: bifurcation theory and catastrophe theory. Readers will be gradually introduced to the language and formalisms of nonlinear sciences, which constitute the framework to describe complex systems. The difficulty with complex systems is that their evolution cannot be fully predicted because of the interdependence and interactions between their different components.

Starting with simple examples and working toward an increasing level of universalization, the work explores diverse scenarios of bifurcations and elementary catastrophes which characterize the qualitative behavior of nonlinear systems. The study of temporal evolution is undertaken using the equations that characterize stationary or oscillatory solutions, while spatial analysis introduces the fascinating problem of morphogenesis.

Accessible to undergraduate university students in any discipline concerned with nonlinear phenomena (physics, mathematics, chemistry, geology, economy, etc.), this work provides a wealth of information for teachers and researchers in these various fields.

Chaouqi Misbah is a senior researcher at the CNRS (National Centre of Scientific Research in France). His work spans from pattern formation in nonlinear science to complex fluids and biophysics. In 2002 he received a major award from the French Academy of Science for his achievements and in 2003 Grenoble University honoured him with a gold medal. Leader of a group of around 40 scientists, he is a member of the editorial board of the French Academy of Science since 2013 and also holds numerous national and international responsibilities.

✦ Table of Contents

Front Matter....Pages I-XIX
Presentation of Main Ideas....Pages 1-13
Basic Introduction to Bifurcations in 1-D....Pages 15-34
The Other Generic Bifurcations....Pages 35-88
Classification of the Seven Elementary Catastrophes....Pages 89-114
Hopf Bifurcation....Pages 115-138
Universal Amplitude Equation in the Neighborhood of a Hopf Bifurcation....Pages 139-159
Parametric Instabilities and Other Nonlinear Behaviors....Pages 161-185
Introduction to Chaos....Pages 187-233
Pattern Formation in One Dimension....Pages 235-272
Universality of Pattern Description near Threshold....Pages 273-295
Fronts between Domains and Invasion of One State by Another....Pages 297-318
Order and Disorder both Spatial and Temporal near a Hopf Bifurcation....Pages 319-338
Two Dimensional Patterns....Pages 339-365
Wavelength Selection....Pages 367-380
Conclusion....Pages 381-390
Solutions to Exercises....Pages 391-452
Back Matter....Pages 453-463

✦ Subjects

Applications of Nonlinear Dynamics and Chaos Theory;Mathematical Methods in Physics;Complex Systems;Biological and Medical Physics, Biophysics