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© 2016

Nonlinear Resonances

Benefits

  • Written by leading experts in the field

  • Offers a systematic overview of all types of resonances and anti-resonances in dynamical systems

  • Provides detailed mathematical derivations and numerical techniques

Book

Part of the Springer Series in Synergetics book series (SSSYN)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 1-38
  3. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 39-81
  4. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 83-117
  5. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 119-137
  6. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 139-160
  7. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 161-201
  8. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 203-223
  9. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 225-240
  10. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 241-260
  11. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 261-291
  12. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 293-331
  13. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 333-350
  14. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 351-366
  15. Shanmuganathan Rajasekar, Miguel A. F. Sanjuan
    Pages 367-390
  16. Back Matter
    Pages 391-409

About this book

Introduction

This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years.

Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others.

The book is self-contained, providing the details of mathematical derivations and techniques involved in numerical simulations. Though primarily intended for graduate students, it can also be considered a reference book for any researcher interested in the dynamics of resonant phenomena.

Keywords

Coupled oscillators Ghost resonance Parametric resonance Resonance and synchronization Resonances in nonlinear systems Stochastic resonance Vibrational resonance

Authors and affiliations

  1. 1.School of PhysicsBharathidasan University TiruchirappalliIndia
  2. 2.Department of PhysicsUniversidad Rey Juan CarlosMóstolesSpain

About the authors

Miguel Sanjuan is full professor of physics at the Universidad Rey Juan Carlos in Madrid, Spain, where he founded the Physics Department in 2006. He is a corresponding member of the Spanish Royal Academy of Sciences, section physics and chemistry, and a foreign member of the Lithuanian Academy of Sciences in the areas of physics and mechanical engineering. Prof. Sanjuan is presently the head of the Nonlinear Dynamics, Chaos and Complex Systems Research Group at the Universidad Rey Juan Carlos.

Shanmuganathan Rajasekar is full professor at the School of Physics, Bharathidasan University, India. He received the Ph.D. degree in Physics (Nonlinear Dynamics) in 1992 under the supervision of Prof. M. Lakshmanan with whom, he co-authored the Springer textbook Nonlinear Dynamics: Integrability, Chaos and Patterns. His recent research focuses on nonlinear dynamics with a special emphasis on nonlinear resonances.

Bibliographic information

Reviews

“The authors have identified a really remarkable set of modern-day topics which resonate (pun inevitable and intended) with the main themes of the book. … The book is intended for graduate students but, as suggested in the book, one is confident that it will find a ready market amongst researchers in the broad area of nonlinear dynamics who require an accessible reference work on nonlinear resonances. The authors of this volume have performed a valuable service for that community.” (K. Alan Shore, Contemporary Physics, Vol. 57 (4), 2016)