Delay-Coupled Complex Systems: and Applications to Lasers

✍ Scribed by Valentin Flunkert (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2011
• Tongue: English
• Leaves: 195
• Series: Springer Theses
• Edition: 1
• Category: Library

✦ Synopsis

This thesis deals with the effects of time-delay in complex nonlinear systems and in particular with its applications in complex networks, and relates it to control theory and nonlinear optics. Delays arise naturally in networks of coupled systems due to finite signal propagation speeds and are thus a key issue in many areas of physics, biology, medicine, and technology. Synchronization phenomena in these networks play an important role, e.g., in the context of learning, cognitive and pathological states in the brain, for secure communication with chaotic lasers or gene regulation. The work includes both novel results on the control of complex dynamics by time-delayed feedback and new fundamental insights into the interplay of delay and synchronization. One of the most interesting results here is a solution to the problem of complete synchronization in general networks with large coupling delay, i.e., large distances between the nodes, by giving a universal classification of networks which has a wide range of interdisciplinary applications.

✦ Table of Contents

Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Introduction....Pages 3-6
Time-Delayed Feedback Control....Pages 7-10
Counterexample....Pages 11-25
Odd-Number Orbits Close to a Fold Bifurcation....Pages 27-34
Towards Stabilization of Odd-Number Orbits in Experiments....Pages 35-44
Stabilization with Symmetric Feedback Matrices....Pages 45-53
Application to Laser Systems....Pages 55-66
Stabilization of Anti-Phase Orbits....Pages 67-85
Front Matter....Pages 87-87
Introduction....Pages 89-91
Structure of the Master Stability Function for Large Delay....Pages 93-109
Lang Kobayashi Laser Equations....Pages 111-119
Necessary Conditions for Synchronization of Lasers....Pages 121-135
Bubbling....Pages 137-147
Summary and Conclusions....Pages 149-150
Front Matter....Pages 151-151
Delay Differential Equations....Pages 153-163
Pydelay: A Simulation Package....Pages 165-178
Back Matter....Pages 179-180

✦ Subjects

Statistical Physics, Dynamical Systems and Complexity;Theoretical, Mathematical and Computational Physics;Laser Technology, Photonics;Control