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E-grāmata: Nonlinear Resonances

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  • Formāts: PDF+DRM
  • Sērija : Springer Series in Synergetics
  • Izdošanas datums: 30-Nov-2015
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319248868
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Nonlinear ResonancesPalielināt
  • Formāts: PDF+DRM
  • Sērija : Springer Series in Synergetics
  • Izdošanas datums: 30-Nov-2015
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319248868
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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.

Preface.- Harmonic and Nonlinear Resonances.- Stochastic Resonance.- Vibrational Resonance in Monostable Systems.- Vibrational Resonance in Multistable and Excitable Systems.- Vibrational and Stochastic Resonances in Spatially Periodic Systems.- Nonlinear and Vibrational Resonances in Time-Delayed Systems.- Signal Propagation in Unidirectionally Coupled.- Experimental Observation of Vibrational Resonance.- Ghost Resonances.- Parametric Resonance.- Autoresonance Resonance.- Slow Passage Through Resonance and Resonance Tongues.- Anti-Resonances.- Appendices.

Recenzijas

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)

1 Harmonic and Nonlinear Resonances
1(38)
1.1 Simple Examples of Resonance
2(2)
1.1.1 What is the Effect of Resonance?
3(1)
1.1.2 Realization of Periodic Forces
3(1)
1.2 Nonlinear Resonance in the Duffing Oscillator
4(8)
1.2.1 Theoretical Equation for the Amplitude of Oscillation
5(1)
1.2.2 Resonance in a Linear System
6(1)
1.2.3 Hysteresis and Jump Phenomenon in the Duffing Oscillator
7(3)
1.2.4 Analog Circuit Simulation
10(1)
1.2.5 Resonance in the Overdamped Duffing Oscillator
11(1)
1.3 Pendulum System
12(2)
1.4 Morse Oscillator
14(2)
1.5 Linear and Nonlinear Jerk Systems
16(3)
1.6 Van der Pol Oscillator
19(5)
1.6.1 Theoretical Treatment
19(1)
1.6.2 Numerical Verification
20(2)
1.6.3 Analog Circuit Simulation
22(2)
1.7 Resonance in Micro-and Nano-Electromechanical Resonators
24(4)
1.7.1 A Double Clamped 3C-SiC Nanoscale Beam
25(2)
1.7.2 A Doubly Clamped Cr-Au Bilayer NEM Resonator
27(1)
1.8 Some Other Examples of Resonance
28(1)
1.8.1 Resonance Magnetoelectric Effect
28(1)
1.8.2 Nonlinear Resonance Ultrasonic Spectroscopy
28(1)
1.8.3 Crack Breathing and Resonance
29(1)
1.9 Quantum Resonance
29(3)
1.10 Applications of Resonance
32(2)
1.11 Resonance Disaster
34(1)
1.12 Concluding Remarks
35(4)
References
36(3)
2 Stochastic Resonance
39(44)
2.1 Characterization of Stochastic Resonance
40(1)
2.2 Stochastic Resonance in Duffing Oscillator
41(8)
2.2.1 Time-Series Plot
42(2)
2.2.2 Mean Residence Time
44(1)
2.2.3 Power Spectrum and SNR
45(2)
2.2.4 Probability Distribution of Residence Times
47(2)
2.3 Theory of Stochastic Resonance
49(6)
2.3.1 Analytical Expression for Power Spectrum
50(3)
2.3.2 Determination of Signal-to-Noise Ratio
53(2)
2.4 Stochastic Resonance in a Coupled Oscillator
55(2)
2.5 Stochastic Resonance in a Magnetic System
57(4)
2.6 Stochastic Resonance in a Monostable System
61(3)
2.7 Linear Systems with Additive and Multiplicative Noises
64(5)
2.7.1 Effect of Additive Noise Only
64(1)
2.7.2 Effect of Multiplicative Noise Only
64(2)
2.7.3 Effect of Multiplicative and Additive Noises
66(3)
2.8 Stochastic Resonance in Quantum Systems
69(2)
2.8.1 A Particle in a Double-Well Potential
69(1)
2.8.2 A Double Quantum Dot System
70(1)
2.9 Applications of Stochastic Resonance
71(6)
2.9.1 Vibration Energy Harvesting
72(1)
2.9.2 Stochastic Encoding
72(1)
2.9.3 Weak Signal Detection
73(1)
2.9.4 Detection of Weak Visual and Brain Signals
73(2)
2.9.5 Stochastic Resonance in Sensory and Animal Behaviour
75(1)
2.9.6 Human Psychophysics Experiments
75(1)
2.9.7 Noise in Human Muscle Spindles and Hearing
76(1)
2.9.8 Electrophysiological Signals
76(1)
2.9.9 Stochastic Resonance in Raman and X-Ray Spectra
77(1)
2.10 Noise-Induced Stochastic Resonance Versus Noise-Induced Synchronization
77(1)
2.11 Concluding Remarks
78(5)
References
78(5)
3 Vibrational Resonance in Monostable Systems
83(36)
3.1 Duffing Oscillator
84(5)
3.1.1 Theoretical Description of Vibrational Resonance
85(2)
3.1.2 Analysis of Vibrational Resonance
87(2)
3.2 Effect of High-Frequency Force in a Linear System
89(1)
3.3 Quintic Oscillator
90(10)
3.3.1 Theoretical Expression for the Response Amplitude
92(1)
3.3.2 Single-Well Potential (ω2/0, β, γ > 0)
93(3)
3.3.3 Single-Well Potential (ω2/0, γ > 0, β < 0, β2 < 4ω2/0γ)
96(1)
3.3.4 Double-Hump Single-Well Potential (ω2/0 > 0, β-Arbitrary, γ < 0)
97(3)
3.4 Asymmetric Duffing Oscillator
100(5)
3.4.1 Theoretical Expression for Response Amplitude
101(1)
3.4.2 Asymmetry Induced Additional Resonance
102(1)
3.4.3 Resonance with Nonsinusoidal Periodic Forces
103(2)
3.4.4 Effect of Noise on Resonance
105(1)
3.5 Overdamped Asymmetric Duffing Oscillator
105(1)
3.6 Morse Oscillator
106(4)
3.7 Quantum Mechanical Morse Oscillator
110(4)
3.8 Significance of Biharmonic Signals
114(1)
3.9 Concluding Remarks
115(4)
References
116(3)
4 Vibrational Resonance in Multistable and Excitable Systems
119(20)
4.1 Underdamped Double-Well Duffing Oscillator
120(7)
4.1.1 Theoretical Approach
121(1)
4.1.2 Vibrational Resonance for α1 = α2 = 1
122(3)
4.1.3 Role of Depth of the Potential Wells
125(1)
4.1.4 Role of Location of the Minima of the Potential
126(1)
4.2 Overdamped Double-Well Duffing Oscillator
127(1)
4.3 Resonance in a Triple-Well Potential System
128(3)
4.4 Vibrational Resonance in an Excitable System
131(3)
4.5 Stochastic Resonance in FitzHugh-Nagumo Equation
134(2)
4.6 Concluding Remarks
136(3)
References
136(3)
5 Vibrational and Stochastic Resonances in Spatially Periodic Systems
139(22)
5.1 Vibrational Resonance in Underdamped Pendulum System
140(5)
5.1.1 Analytical Expression for the Response Amplitude Q
140(2)
5.1.2 Connection Between Resonance and ωr
142(1)
5.1.3 Role of Stability of the Equilibrium Points
143(2)
5.2 Vibrational Resonance in Overdamped Pendulum System
145(1)
5.3 Vibrational Resonance in a Modified Chua's Circuit Equation
146(6)
5.3.1 The Modified Chua's Circuit Model Equation
146(2)
5.3.2 Role of Number of Breakpoints N on Resonance
148(2)
5.3.3 Jump Phenomenon
150(2)
5.3 Stochastic Resonance in the Pendulum System
152(3)
5.5 Stochastic Resonance in a Multi-Scroll Chua's Circuit Equation
155(3)
5.6 Comparison Between Stochastic and Vibrational Resonances
158(1)
5.7 Concluding Remarks
159(2)
References
160(1)
6 Nonlinear and Vibrational Resonances in Time-Delayed Systems
161(42)
6.1 Time-Delay is Ubiquitous
162(2)
6.2 Nonlinear Resonance in Time-Delayed Duffing Oscillator
164(5)
6.2.1 Theoretical Expression for Response Amplitude
164(2)
6.2.2 Response Amplitude A Versus the Control Parameters ω, γ and α
166(3)
6.3 Resonance in a Linear System with Time-Delayed Feedback
169(2)
6.4 Vibrational Resonance in an Underdamped and Time-Delayed Duffing Oscillator
171(6)
6.4.1 Theoretical Expression for the Response Amplitude Q
171(1)
6.4.2 Resonance Analysis in the Double-Well System
172(4)
6.4.3 Resonance Analysis in the Single-Well System
176(1)
6.5 Vibrational Resonance in an Overdamped Duffing Oscillator
177(3)
6.6 Some Common Effects of Time-Delayed Feedback
180(2)
6.7 Effect of Multi Time-Delayed Feedback
182(3)
6.8 Vibrational Resonance with Some Other Time-Delayed Feedbacks
185(13)
6.8.1 Gamma Distributed Time-Delayed Feedback
185(3)
6.8.2 Integrative Time-Delayed Feedback
188(2)
6.8.3 State-Dependent Time-Delayed Feedback
190(5)
6.8.4 Feedback with Random Time-Delay
195(3)
6.9 Concluding Remarks
198(5)
References
198(5)
7 Signal Propagation in Unidirectionally Coupled Systems
203(22)
7.1 Significance of Unidirectional Coupling
204(2)
7.2 Nonlinear Resonance and Signal Propagation
206(5)
7.2.1 Theoretical Treatment
206(2)
7.2.2 Analysis of Effect of One-Way Coupling
208(3)
7.2.3 Unidirectionally Coupled Linear Systems
211(1)
7.3 Vibrational Resonance and Signal Propagation
211(6)
7.3.1 Theoretical Treatment
212(2)
7.3.2 Effect of δ and g on Qi
214(3)
7.4 Stochastic Resonance and Signal Propagation
217(5)
7.4.1 One-Way Coupled Bellows Map
217(1)
7.4.2 Numerical Results
218(4)
7.5 Concluding Remarks
222(3)
References
222(3)
8 Experimental Observation of Vibrational Resonance
225(16)
8.1 Single Chua's Circuit
226(4)
8.2 Analog Simulation of the Overdamped Bistable System
230(2)
8.3 Vertical Cavity Surface Emitting Laser System
232(3)
8.4 An Excitable Electronic Circuit
235(1)
8.5 Unidirectionally Coupled Chua's Circuits
236(3)
8.6 Concluding Remarks
239(2)
References
239(2)
9 Ghost Resonances
241(20)
9.1 Ghost-Stochastic Resonance in a Single System
242(5)
9.1.1 System with Periodic Forces
242(3)
9.1.2 System with Aperiodic Forces
245(2)
9.2 Ghost-Stochastic Resonance in a Network System
247(2)
9.3 Ghost-Vibrational Resonance in a Single System
249(4)
9.3.1 Theoretical Calculation of Q(ω0)
250(3)
9.4 Effect of k, n and Δω0 on Resonance
253(2)
9.5 Ghost-Vibrational Resonance in a Network System
255(3)
9.5.1 Description of the Network Model
255(1)
9.5.2 Undamped Signal Propagation
255(2)
9.5.3 A Network with All the Units Driven by External Forces
257(1)
9.6 Ghost-Vibrational Resonance in Chua's Circuit
258(1)
9.7 Concluding Remarks
259(2)
References
260(1)
10 Parametric Resonance
261(32)
10.1 Examples of Parametric Resonance
262(1)
10.2 Parametric Instability in a Linear System
263(7)
10.2.1 Illustration of Parametric Resonance
264(3)
10.2.2 Theoretical Treatment
267(1)
10.2.3 Analog Simulation
268(2)
10.3 Parametrically Driven Pendulum
270(6)
10.3.1 Effective Parametric Resonance
274(2)
10.4 The Quasiperiodic Mathieu Equation
276(4)
10.5 Quantum Parametric Resonance in a Two-Coupled Systems
280(5)
10.6 Applications
285(3)
10.6.1 Parametric Resonance Based Scanning Probe Microscopy
287(1)
10.7 Concluding Remarks
288(5)
References
289(4)
11 Autoresonance
293(40)
11.1 Illustration of Autoresonance
294(1)
11.2 Threshold Analysis
295(4)
11.3 Parametric Autoresonance in the Duffing Oscillator
299(8)
11.3.1 Approximate Solution
300(1)
11.3.2 Analytical Theory of Parametric Autoresonance
301(2)
11.3.3 Dynamics in the Neighbourhood of (I*, ψ*)
303(2)
11.3.4 Analytical Solution of Equation (11.33)
305(1)
11.3.5 Dynamics for Arbitrary Initial Conditions
306(1)
11.3.6 Effect of Damping
306(1)
11.4 Autoresonance and Limiting Phase Trajectories
307(7)
11.4.1 Approximate Solution
308(1)
11.4.2 Limiting Phase Trajectories
309(4)
11.4.3 Autoresonance
313(1)
11.5 Autoresonance in Optical Guided Waves
314(2)
11.6 Energy Conversion in a Four-Wave Mixing
316(3)
11.7 Autoresonance in a Nonlinear Wave System
319(3)
11.8 A Quantum Analogue of Autoresonance
322(4)
11.9 Applications
326(3)
11.10 Concluding Remarks
329(4)
References
329(4)
12 Coherence and Chaotic Resonances
333(18)
12.1 An Illustration of Coherence Resonance
334(2)
12.2 Mechanism of Coherence Resonance
336(1)
12.3 Coherence Resonance in a Modified Chua's Circuit Model Equations
337(3)
12.4 Theory of Coherence Resonance
340(4)
12.4.1 A Two-State Model
341(3)
12.5 Chaotic Resonance
344(5)
12.5.1 Generating Similar Noise and Chaos
345(2)
12.5.2 Effect of Chaotic Perturbations
347(2)
12.6 Conclusion
349(2)
References
349(2)
13 Slow Passage Through Resonance and Resonance Tongues
351(16)
13.1 Passage Through Resonance in Duffing Oscillator
352(4)
13.2 Mathieu Equation with Parametric Perturbation
356(7)
13.2.1 Single Parametric Resonance
356(2)
13.2.2 Theoretical Treatment
358(2)
13.2.3 Two Parametric Resonance
360(3)
13.2.4 Three Resonance Tongues
363(1)
13.3 Nonlinear Systems with Parametric Perturbation
363(2)
13.4 Concluding Remarks
365(2)
References
366(1)
14 Antiresonances
367(24)
14.1 Multiple Resonance and Antiresonance in Coupled Systems
368(10)
14.1.1 Theoretical Treatment for Two-Coupled Oscillators
369(1)
14.1.2 Resonance and Antiresonance in a Linear System
370(2)
14.1.3 Two-Coupled Duffing Oscillators
372(3)
14.1.4 Analog Simulation of Two-Coupled Duffing Oscillators
375(2)
14.1.5 Response of n-Coupled Oscillators
377(1)
14.2 Parametric Antiresonance
378(4)
14.2.1 Parametrically Driven van der Pol Oscillator
379(3)
14.3 Suppression of Parametric Resonance
382(3)
14.4 Stochastic Antiresonance
385(2)
14.5 Coherence Antiresonance
387(1)
14.6 Concluding Remarks
388(3)
References
389(2)
A Classification of Equilibrium Points of Two-Dimensional Systems
391(4)
Reference
393(2)
B Roots of a Cubic Equation
395(4)
Reference
397(2)
C Analog Circuit Simulation of Ordinary Differential Equations
399(8)
C.1 Building Blocks of an Analog Circuit
399(4)
C.1.1 Inverting Amplifier
400(1)
C.1.2 An Inverting Summing Amplifier
400(1)
C.1.3 A Subtractor
401(1)
C.1.4 An Integrator
401(1)
C.1.5 Multiplier
402(1)
C.2 Analog Circuit for Duffing Oscillator Equation
403(4)
References
405(2)
Index 407
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.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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