Dynamics of Nonlinear Time-Delay Systems

✍ Scribed by Muthusamy Lakshmanan, Dharmapuri Vijayan Senthilkumar (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2011
• Tongue: English
• Leaves: 332
• Series: Springer Series in Synergetics
• Edition: 1
• Category: Library

✦ Synopsis

Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularlysuitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finiteswitching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant

✦ Table of Contents

Front Matter....Pages i-xvii
Delay Differential Equations....Pages 1-15
Linear Stability and Bifurcation Analysis....Pages 17-29
Bifurcation and Chaos in Time-Delayed Piecewise Linear Dynamical System....Pages 31-54
A Few Other Interesting Chaotic Delay Differential Equations....Pages 55-84
Implications of Delay Feedback: Amplitude Death and Other Effects....Pages 85-103
Recent Developments on Delay Feedback/Coupling: Complex Networks, Chimeras, Globally Clustered Chimeras and Synchronization....Pages 105-126
Complete Synchronization of Chaotic Oscillations in Coupled Time-Delay Systems....Pages 127-138
Transition from Anticipatory to Lag Synchronization via Complete Synchronization....Pages 139-164
Intermittency Transition to Generalized Synchronization....Pages 165-199
Transition from Phase to Generalized Synchronization....Pages 201-226
DTM Induced Oscillating Synchronization....Pages 227-250
Exact Solutions of Certain Time Delay Systems: The Car-Following Models....Pages 251-258
Back Matter....Pages 259-313

✦ Subjects

Nonlinear Dynamics;Vibration, Dynamical Systems, Control;Systems Theory, Control;Appl.Mathematics/Computational Methods of Engineering;Complex Networks;Circuits and Systems