"Dynamics of Nonlinear Time-Delay Systems" by M. Lakshmanan · D.V. Senthilkumar

This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics

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.
Special attention is devoted to scalar chaotic/hyperchaotic time-delaysystems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions.
Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics and the detailed presentation of real-world applications.


Contents
Preface
1 Delay Differential Equations
2 Linear Stability and Bifurcation Analysis
3 Bifurcation and Chaos in Time-Delayed Piecewise Linear Dynamical System
4 A Few Other Interesting Chaotic Delay Differential Equations
5 Implications of Delay Feedback: Amplitude Death and Other Effects
6 Recent Developments on Delay Feedback/Coupling: Complex Networks, Chimeras, Globally Clustered Chimeras and Synchronization
7 Complete Synchronization of Chaotic Oscillations in Coupled Time-Delay Systems
8 Transition from Anticipatory to Lag Synchronization via Complete Synchronization
9 Intermittency Transition to Generalized Synchronization
10 Transition from Phase to Generalized Synchronization
11 DTM Induced Oscillating Synchronization
12 Exact Solutions of Certain Time Delay Systems: The Car-Following Models
A: Computing Lyapunov Exponents for Time-Delay Systems
B: A Brief Introduction to Synchronization in Chaotic Dynamical Systems
C: Recurrence Analysis
D: Some More Examples of DDEs
Glossary