Dynamics of nonlinear time-delay systems / M. Lakshmanan, D.V. Senthilkumar.

Format:

Book

Author/Creator:

Lakshmanan, M. (Muthusamy)

Contributor:

Senthilkumar, D. V.

Series:

Springer series in synergetics.

Springer complexity.

Springer series in synergetics, 0172-7389

Springer complexity

Language:

English

Subjects (All):

Nonlinear systems.

Delay lines.

Physical Description:

1 online resource (321 p.)

Edition:

1st ed. 2011.

Place of Publication:

Berlin : Springer-Verlag, 2010.

Language Note:

English

Summary:

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 particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching 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. 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. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, 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:

Delay Differential Equations

Linear Stability and Bifurcation Analysis

Bifurcation and Chaos in Time-delayed Piecewise Linear

A Few Other Interesting Chaotic Delay Differential Equations

Implications of Delay Feebdack: Amplitude Death and Other Effects

Recent Developments on Delay Feedback/Coupling: Complex

Complete Synchronization in Coupled Time-delay Systems

Transition from Anticipatory to Lag Synchronization via Complete

Intermittency Transition to Generalized Snychronization

Transition from Phase to Generalized Synchronization

DTM Induced Oscillating Synchronization

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

References

Glossary

Index.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-283-07747-7

9786613077479

3-642-14938-3

OCLC:

701718785