Nonlinear Resonances

Front Cover
Springer, Nov 30, 2015 - Science - 409 pages

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.

 

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Contents

1 Harmonic and Nonlinear Resonances
1
2 Stochastic Resonance
39
3 Vibrational Resonance in Monostable Systems
82
4 Vibrational Resonance in Multistable and Excitable Systems
119
5 Vibrational and Stochastic Resonances in Spatially Periodic Systems
138
6 Nonlinear and Vibrational Resonances in TimeDelayed Systems
161
7 Signal Propagation in Unidirectionally Coupled Systems
203
8 Experimental Observation of Vibrational Resonance
224
11 Autoresonance
293
12 Coherence and Chaotic Resonances
332
13 Slow Passage Through Resonance and Resonance Tongues
351
14 Antiresonances
367
A Classification of Equilibrium Points of TwoDimensional Systems
391
B Roots of a Cubic Equation
395
C Analog Circuit Simulation of Ordinary Differential Equations
398
Index
406

9 Ghost Resonances
241
10 Parametric Resonance
261

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About the author (2015)

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.