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Nonlinear Dynamics: Integrability, Chaos and Patterns Softcover reprint of the original 1st ed. 2003 [Mīkstie vāki]

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  • Formāts: Paperback / softback, 620 pages, height x width: 235x155 mm, weight: 973 g, XX, 620 p., 1 Paperback / softback
  • Sērija : Advanced Texts in Physics
  • Izdošanas datums: 28-Oct-2012
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642628729
  • ISBN-13: 9783642628726
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Nonlinear Dynamics: Integrability, Chaos and Patterns Softcover reprint of the original 1st ed. 2003Palielināt
  • Formāts: Paperback / softback, 620 pages, height x width: 235x155 mm, weight: 973 g, XX, 620 p., 1 Paperback / softback
  • Sērija : Advanced Texts in Physics
  • Izdošanas datums: 28-Oct-2012
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642628729
  • ISBN-13: 9783642628726
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783642628726.html
Keywords:
Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics. These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics, mathematics, engineering and applied sciences who wish to gain a broad knowledge of nonlinear dynamics. It describes fundamental concepts, theoretical procedures, experimental and numerical techniques and technological applications of nonlinear dynamics. Numerous examples and problems are included to facilitate the understanding of the concepts and procedures described. In addition to 16 chapters of main material, the book contains 10 appendices which present in-depth mathematical formulations involved in the analysis of various nonlinear systems.

Recenzijas

From the reviews:









"The authors must be congratulated . The book contains many examples, exercises and problems. Many technical details are relegated to appendices, making the main text highly readable. There are a large number of nice figures and illustrations, which complement the text very well. I feel that this book would be a valuable addition to a personal or departmental library. I believe that this book has the potential to become a standard text in the field of non-linear dynamics." (Sanjay Puri, International Journal of Robust and Nonlinear Control, Vol. 15 (11), 2005)



"The book is an extensive treatise of nonlinear dynamical systems with emphasis on the concepts of chaos, integrability and patterns. the book contains numerous examples and exercises divided in two groups by their difficulty." (Peter Polacik, Zentralblatt MATH, Vol. 1038 (13), 2004)



"The book gives a comprehensive introduction to the different fields in nonlinear dynamics, such as chaos, fractals, integrability and soliton theory. It also includes a large number of interesting applications. Each chapter and the appendix include a number of exercises. the book can be highly recommended for beginners in these fields since it provides a good survey of the different fields in nonlinear dynamics." (W.-H. Steeb, Mathematical Reviews, 2004 d)



"Undoubtedly, the best survey text on Nonlinear Dynamics available today. the survey is carefully balanced, with detail and clarity, to enable students and researchers from other fields to learn the salient tools. For advanced undergraduate students and graduate research students looking for just one book in Nonlinear Dynamics, here is the one to get. It is precisely the book that has been needed to provide students with the fundamental knowledge across the landscape of Nonlinear Dynamics ." (B I Henry, The Physicist, Vol. 40 (4), 2003)

Papildus informācija

Springer Book Archives
1 What is Nonlinearity?
1(16)
1.1 Dynamical Systems: Linear and Nonlinear Forces
2(3)
1.2 Mathematical Implications of Nonlinearity
5(5)
1.2.1 Linear and Nonlinear Systems
5(2)
1.2.2 Linear Superposition Principle
7(3)
1.3 Working Definition of Nonlinearity
10(1)
1.4 Effects of Nonlinearity
11(6)
2 Linear and Nonlinear Oscillators
17(14)
2.1 Linear Oscillators and Predictability
17(4)
2.1.1 Free Oscillations
18(1)
2.1.2 Damped Oscillations
19(1)
2.1.3 Damped and Forced Oscillations
20(1)
2.2 Damped and Driven Nonlinear Oscillators
21(6)
2.2.1 Free Oscillations
22(1)
2.2.2 Damped Oscillations
23(1)
2.2.3 Forced Oscillations -- Primary Resonance and Jump Phenomenon (Hysteresis)
23(3)
2.2.4 Secondary Resonances (Subharmonic and Superharmonic)
26(1)
2.3 Nonlinear Oscillations and Bifurcations
27(4)
Problems
29(2)
3 Qualitative Features
31(44)
3.1 Autonomous and Nonautonomous Systems
32(2)
3.2 Dynamical Systems as Coupled First-Order Differential Equations: Equilibrium Points
34(2)
3.3 Phase Space/Phase Plane and Phase Trajectories: Stability, Attractors and Repellers
36(2)
3.4 Classification of Equilibrium Points: Two-Dimensional Case
38(12)
3.4.1 General Criteria for Stability
38(2)
3.4.2 Classification of Equilibrium (Singular) Points
40(10)
3.5 Limit Cycle Motion -- Periodic Attractor
50(4)
3.5.1 Poincare-Bendixson Theorem
52(2)
3.6 Higher Dimensional Systems
54(4)
3.6.1 Example: Lorenz Equations
55(3)
3.7 More Complicated Attractors
58(7)
3.7.1 Torus
59(3)
3.7.2 Quasiperiodic Attractor
62(1)
3.7.3 Poincare Map
63(1)
3.7.4 Chaotic Attractor
64(1)
3.8 Dissipative and Conservative Systems
65(4)
3.8.1 Hamiltonian Systems
68(1)
3.9 Conclusions
69(6)
Problems
69(6)
4 Bifurcations and Onset of Chaos in Dissipative Systems
75(48)
4.1 Some Simple Bifurcations
76(13)
4.1.1 Saddle-Node Bifurcation
77(3)
4.1.2 The Pitchfork Bifurcation
80(3)
4.1.3 Transcritical Bifurcation
83(2)
4.1.4 Hopf Bifurcation
85(4)
4.2 Discrete Dynamical Systems
89(18)
4.2.1 The Logistic Map
90(1)
4.2.2 Equilibrium Points and Their Stability
91(1)
4.2.3 Stability When the First Derivative
Equals to +1 or --1
92(2)
4.2.4 Periodic Solutions or Cycles
94(2)
4.2.5 Period Doubling Phenomenon
96(2)
4.2.6 Onset of Chaos: Sensitive Dependence on Initial Conditions -- Lyapunov Exponent
98(3)
4.2.7 Bifurcation Diagram
101(2)
4.2.8 Bifurcation Structure in the Interval 3.57 ≤ a ≤ 4
103(1)
4.2.9 Exact Solution at a = 4
104(1)
4.2.10 Logistic Map: A Geometric Construction of the Dynamics -- Cobweb Diagrams
105(2)
4.3 Strange Attractor in the Henon Map
107(4)
4.3.1 The Period Doubling Phenomenon
108(2)
4.3.2 Self-Similar Structure
110(1)
4.4 Other Routes to Chaos
111(12)
4.4.1 Quasiperiodic Route to Chaos
111(2)
4.4.2 Intermittency Route to Chaos
113(1)
4.4.3 Type-I Intermittency
114(2)
4.4.4 Standard Bifurcations in Maps
116(2)
Problems
118(5)
5 Chaos in Dissipative Nonlinear Oscillators and Criteria for Chaos
123(36)
5.1 Bifurcation Scenario in Duffing Oscillator
124(11)
5.1.1 Period Doubling Route to Chaos
126(4)
5.1.2 Intermittency Transition
130(2)
5.1.3 Quasiperiodic Route to Chaos
132(1)
5.1.4 Strange Nonchaotic Attractors (SNAs)
133(2)
5.2 Lorenz Equations
135(7)
5.2.1 Period Doubling Bifurcations and Chaos
136(6)
5.3 Some Other Ubiquitous Chaotic Oscillators
142(5)
5.3.1 Driven van der Pol Oscillator
142(1)
5.3.2 Damped, Driven Pendulum
142(3)
5.3.3 Morse Oscillator
145(1)
5.3.4 Rossler Equations
146(1)
5.4 Necessary Conditions for Occurrence of Chaos
147(4)
5.4.1 Continuous Time Dynamical Systems (Differential Equations)
147(1)
5.4.2 Discrete Time Systems (Maps)
148(3)
5.5 Computational Chaos, Shadowing and All That
151(2)
5.6 Conclusions
153(6)
Problems
153(6)
6 Chaos in Nonlinear Electronic Circuits
159(32)
6.1 Linear and Nonlinear Circuit Elements
159(2)
6.2 Linear Circuits: The Resonant RLC Circuit
161(4)
6.3 Nonlinear Circuits
165(6)
6.3.1 Chua's Diode: Autonomous Case
165(2)
6.3.2 A Simple Practical Implementation of Chua's Diode
167(1)
6.3.3 Bifurcations and Chaos
167(4)
6.4 Chaotic Dynamics of the Simplest Dissipative Nonautonomous Circuit: Murali-Lakshmanan-Chua (MLC) Circuit
171(7)
6.4.1 Experimental Realization
171(1)
6.4.2 Stability Analysis
172(1)
6.4.3 Explicit Analytical Solutions
173(1)
6.4.4 Experimental and Numerical Studies
174(4)
6.5 Analog Circuit Simulations
178(3)
6.6 Some Other Useful Nonlinear Circuits
181(4)
6.6.1 RL Diode Circuit
181(1)
6.6.2 Hunt's Nonlinear Oscillator
182(1)
6.6.3 p-n Junction Diode Oscillator
182(1)
6.6.4 Modified Chua Circuit
182(2)
6.6.5 Colpitt's Oscillator
184(1)
6.7 Nonlinear Circuits as Dynamical Systems
185(6)
Problems
185(6)
7 Chaos in Conservative Systems
191(44)
7.1 Poincare Cross Section or Surface of Section
192(4)
7.2 Possible Orbits in Conservative Systems
196(8)
7.2.1 Regular Trajectories
197(4)
7.2.2 Irregular Trajectories
201(1)
7.2.3 Canonical Perturbation Theory: Overlapping Resonances and Chaos
202(2)
7.3 Henon-Heiles System
204(9)
7.3.1 Equilibrium Points
206(1)
7.3.2 Poincare Surface of Section of the System
207(1)
7.3.3 Numerical Results
208(5)
7.4 Periodically Driven Undamped Duffing Oscillator
213(3)
7.5 The Standard Map
216(10)
7.5.1 Linear Stability and Invariant Curves
217(5)
7.5.2 Numerical Analysis: Regular and Chaotic Motions
222(4)
7.6 Kolmogorov-Arnold-Moser Theorem
226(1)
7.7 Conclusions
227(8)
Problems
228(7)
8 Characterization of Regular and Chaotic Motions
235(24)
8.1 Lyapunov Exponents
235(3)
8.2 Numerical Computation of Lyapunov Exponents
238(7)
8.2.1 One-Dimensional Map
238(1)
8.2.2 Computation of Lyapunov Exponents for Continuous Time Dynamical Systems
239(6)
8.3 Power Spectrum
245(5)
8.3.1 The Power Spectrum and Dynamical Motion
245(5)
8.4 Autocorrelation
250(3)
8.5 Dimension
253(2)
8.6 Criteria for Chaotic Motion
255(4)
Problems
258(1)
9 Further Developments in Chaotic Dynamics
259(36)
9.1 Time Series Analysis
260(2)
9.1.1 Estimation of Time-Delay and Embedding Dimension
260(1)
9.1.2 Largest Lyapunov Exponent
261(1)
Problems
261(1)
9.2 Stochastic Resonance
262(4)
Problems
264(2)
9.3 Chaotic Scattering
266(3)
Problems
268(1)
9.4 Controlling of Chaos
269(8)
9.4.1 Controlling and Controlling Algorithms
270(1)
9.4.2 Stabilization of UPO
271(3)
Problems
274(3)
9.5 Synchronization of Chaos
277(7)
9.5.1 Chaos in the DVP Oscillator
277(1)
9.5.2 Synchronization of Chaos in the DVP Oscillator
278(2)
9.5.3 Chaotic Signal Masking and Transmission of Analog Signals
280(2)
9.5.4 Chaotic Digital Signal Transmission
282(2)
Problems
284(1)
9.6 Quantum Chaos
284(9)
9.6.1 Quantum Signatures of Chaos
284(3)
9.6.2 Rydberg Atoms and Quantum Chaos
287(2)
9.6.3 Hydrogen Atom in a
Generalized van der Waals Interaction
289(2)
9.6.4 Outlook
291(2)
Problems
293(1)
9.7 Conclusions
293(2)
10 Finite Dimensional Integrable Nonlinear Dynamical Systems
295(46)
10.1 What is Integrability?
296(1)
10.2 The Notion of Integrability
297(3)
10.3 Complete Integrability -- Complex Analytic Integrability
300(5)
10.3.1 Real Time and Complex Time Behaviours
301(1)
10.3.2 Partial Integrability and Constrained Integrability
302(1)
10.3.3 Integrability and Separability
302(3)
10.4 How to Detect Integrability: Painleve Analysis
305(12)
10.4.1 Classification of Singular Points
306(1)
10.4.2 Historical Development of the Painleve Approach and Integrability of Ordinary Differential Equations
307(4)
10.4.3 Painleve Method of Singular Point Analysis for Ordinary Differential Equations
311(6)
10.5 Painleve Analysis and Integrability of Two-Coupled Nonlinear Oscillators
317(4)
10.5.1 Quartic Anharmonic Oscillators
317(4)
10.6 Symmetries and Integrability
321(9)
10.6.1 Invariance Conditions, Determination of Infinitesimals and First Integrals of Motion
323(3)
10.6.2 Application -- The Henon-Heiles System
326(4)
10.7 A Direct Method of Finding Integrals of Motion
330(1)
10.8 Integrable Systems with Degrees of Freedom Greater Than Two
331(2)
10.9 Integrable Discrete Systems
333(2)
10.10 Integrable Dynamical Systems on Discrete Lattices
335(1)
10.11 Conclusion
336(5)
Problems
337(4)
11 Linear and Nonlinear Dispersive Waves
341(18)
11.1 Linear Waves
341(1)
11.2 Linear Nondispersive Wave Propagation
342(1)
11.3 Linear Dispersive Wave Propagation
343(2)
11.4 Fourier Transform and Solution of Initial Value Problem
345(3)
11.5 Wave Packet and Dispersion
348(2)
11.6 Nonlinear Dispersive Systems
350(2)
11.6.1 An Illustration of the Wave of Permanence
350(1)
11.6.2 John Scott Russel's Great Wave of Translation
350(2)
11.7 Cnoidal and Solitary Waves
352(3)
11.7.1 Korteweg-de Vries Equation and the Solitary Waves and Cnoidal Waves
352(3)
11.8 Conclusions
355(4)
Problems
355(4)
12 Korteweg-de Vries Equation and Solitons
359(22)
12.1 The Scott Russel Phenomenon and KdV Equation
359(7)
12.2 The Fermi-Pasta-Ulam Numerical Experiments on Anharmonic Lattice
366(3)
12.2.1 The FPU Lattice
366(2)
12.2.2 FPU Recurrence Phenomenon
368(1)
12.3 The KdV Equation Again!
369(3)
12.3.1 Asymptotic Analysis and the KdV Equation
369(3)
12.4 Numerical Experiments of Zabusky and Kruskal: The Birth of Solitons
372(3)
12.5 Hirota's Director Bilinearization Method for Soliton Solutions of KdV Equation
375(5)
12.6 Conclusions
380(1)
13 Basic Soliton Theory of KdV Equation
381(26)
13.1 The Miura Transformation and Linearization of KdV: The Lax Pair
382(4)
13.1.1 The Miura Transformation
382(1)
13.1.2 Galilean Invariance and Schrodinger Eigenvalue Problem
383(1)
13.1.3 Linearization of the KdV Equation
384(1)
13.1.4 Lax Pair
385(1)
13.2 Lax Pair and the Method of Inverse Scattering: A New Method to Solve the Initial Value Problem
386(4)
13.2.1 The Inverse Scattering Transform (IST) Method for KdV Equation
386(4)
13.3 Explicit Soliton Solutions
390(5)
13.3.1 One-Soliton Solution (N = 1)
390(2)
13.3.2 Two-Soliton Solution
392(1)
13.3.3 N-Soliton Solution
393(1)
13.3.4 Soliton Interaction
394(1)
13.3.5 Nonreflectionless Potentials
395(1)
13.4 Hamiltonian Structure of KdV Equation
395(7)
13.4.1 Dynamics of Continuous Systems
396(2)
13.4.2 KdV as a Hamiltonian Dynamical System
398(1)
13.4.3 Complete Integrability of the KdV Equation
399(3)
13.5 Infinite Number of Conserved Densities
402(1)
13.6 Backlund Transformations
403(2)
13.7 Conclusions
405(2)
14 Other Ubiquitous Soliton Equations
407(48)
14.1 Identification of Some Ubiquitous Nonlinear Evolution Equations from Physical Problems
408(6)
14.1.1 The Nonlinear Schrodinger Equation in Optical Fibers
409(1)
14.1.2 The Sine-Gordon Equation in Long Josephson Junctions
410(2)
14.1.3 Dynamics of Ferromagnets: Heisenberg Spin Equations
412(2)
14.1.4 The Lattice with Exponential Interaction: The Toda Equation
414(1)
14.2 The Zakharov-Shabat (ZS)/Ablowitz-Kaup-Newell-Segur (AKNS)
Linear Eigenvalue Problem and NLEES
414(1)
14.2.1 The AKNS Linear Eigenvalue Problem and AKNS Equations
415(1)
14.2.2 The Standard Soliton Equations
416(2)
14.3 Solitary Wave Solutions and Basic Solitons
418(9)
14.3.1 The MKdV Equation: Pulse Soliton
418(1)
14.3.2 The sine-Gordon Equation: Kink, Antikink and Breathers
419(5)
14.3.3 The Nonlinear Schrodinger Equation: Envelope Soliton
424(1)
14.3.4 The Heisenberg Spin Equation: The Spin Soliton
425(1)
14.3.5 The Toda Lattice: Discrete Soliton
426(1)
14.4 Hirota's Method and Soliton Nature of Solitary Waves
427(7)
14.4.1 The Modified KdV Equation
427(2)
14.4.2 The NLS Equation
429(2)
14.4.3 The sine-Gordon Equation
431(1)
14.4.4 The Heisenberg Spin System
432(2)
14.5 Solutions via IST Method
434(4)
14.5.1 Direct and Inverse Scattering
434(1)
14.5.2 Time Evolution of the Scattering Data
435(1)
14.5.3 Soliton Solutions
436(2)
14.6 Backhand Transformations
438(2)
14.7 Conservation Laws and Constants of Motion
440(4)
14.8 Hamiltonian Structure and Integrability
444(4)
14.8.1 Hamiltonian Structure
444(1)
14.8.2 Complete Integrability of the NLS Equation
445(3)
14.9 Conclusions
448(7)
Problems
451(4)
15 Spatio-Temporal Patterns
455(42)
15.1 Linear Diffusion Equation
456(2)
15.2 Nonlinear Diffusion and Reaction-Diffusion Equations
458(4)
15.2.1 Nonlinear Reaction-Diffusion Equations
459(2)
15.2.2 Dissipative Systems
461(1)
15.3 Spatio-Temporal Patterns in Reaction-Diffusion Systems
462(20)
15.3.1 Homogeneous Patterns
463(1)
15.3.2 Autowaves: Travelling Wave Fronts, Pulses, etc
463(5)
15.3.3 Ring Waves, Spiral Waves and Scroll Waves
468(3)
15.3.4 Turing Instability and Turing Patterns
471(6)
15.3.5 Localized Structures
477(1)
15.3.6 Spatio-Temporal Chaos
478(4)
15.4 Cellular Neural/Nonlinear Networks (CNNs)
482(10)
15.4.1 Cellular Nonlinear Networks (CNNs)
482(2)
15.4.2 Arrays of MLC Circuits: Simple Examples of CNN
484(1)
15.4.3 Active Wave Propagation and its Failure in One-Dimensional CNNs
485(2)
15.4.4 Turing Patterns
487(1)
15.4.5 Spatio-Temporal Chaos
488(4)
15.5 Some Exactly Solvable Nonlinear Diffusion Equations
492(2)
15.5.1 The Burgers Equation
492(1)
15.5.2 The Fokas-Yortsos-Rosen Equation
492(1)
15.5.3 Generalized Fisher's Equation
493(1)
15.6 Conclusion
494(3)
Problems
494(3)
16 Nonlinear Dynamics: From Theory to Technology
497(88)
16.1 Chaotic Cryptography
498(2)
16.1.1 Basic Idea of Cryptography
498(1)
16.1.2 An Elementary Chaotic Cryptographic System
498(2)
16.2 Using Chaos (Controlling) to Calm the Web
500(4)
16.3 Some Other Possibilities of Using Chaos
504(2)
16.3.1 Communicating by Chaos
504(1)
16.3.2 Chaos and Financial Markets
505(1)
16.4 Optical Soliton Based Communications
506(2)
16.5 Soliton Based Optical Computing
508(11)
16.5.1 Photo-Refractive Materials and the Manakov Equation
508(1)
16.5.2 Soliton Solutions and Shape Changing Collisions
509(4)
16.5.3 Optical Soliton Based Computation
513(6)
16.6 Micromagnetics and Magnetoelectronics
519(2)
16.7 Conclusions
521(64)
A Elliptic Functions and Solutions of Certain Nonlinear Equations
523(7)
Problems
530(2)
B Perturbation and Related Approximation Methods
532(1)
B.1 Approximation Methods
For Nonlinear Differential Equations
532(4)
B.2 Canonical Perturbation Theory for Conservative Systems
536(1)
B.2.1 One Degree of Freedom Hamiltonian Systems
536(2)
B.2.2 Two Degrees of Freedom Systems
538(2)
Problems
540(2)
C A Fourth-Order Runge--Kutta Integration Method
542(2)
Problems
544(1)
D Nature of Phase Space Trajectories
For 1, 2 < 0 and 1 < 0 < 2 (Sect. 3.4.2)
545(1)
Problems
546(1)
E Fractals and Multifractals
547(4)
Problems
551(2)
F Spectrum of the sech2αx Potential
553(2)
Problems
555(1)
G Inverse Scattering Transform for the Schrodinger Spectral Problem
556(1)
G.1 The Linear Eigenvalue Problem
556(1)
G.2 The Direct Scattering Problem
557(2)
G.3 The Inverse Scattering Problem
559(2)
G.4 Reconstruction of the Potential
561(1)
Problems
561(1)
H Inverse Scattering Transform for the Zakharov-Shabat Eigenvalue Problem
562(1)
H.1 The Linear Eigenvalue Problem
562(1)
H.2 The Direct Scattering Problem
563(2)
H.3 Inverse Scattering Problem
565(1)
H.4 Reconstruction of the Potentials
566(1)
Problems
567(1)
I Integrable Discrete Soliton Systems
568(1)
I.1 Integrable Finite Dimensional N-Particles System on a Line: Calogero--Moser System
568(2)
I.2 The Toda Lattice
570(2)
I.3 Other Discrete Lattice Systems
572(1)
I.4 Solitary Wave (Soliton) Solution of the Toda Lattice
573(2)
Problems
575(1)
J Painleve Analysis for Partial Differential Equations
576(1)
J.1 The Painleve Property for PDEs
576(1)
J.1.1 Painleve Analysis
577(1)
J.2 Examples
578(1)
J.2.1 KdV Equation
578(3)
J.2.2 The Nonlinear Schrodinger Equation
581(3)
Problems
584(1)
Glossary 585(12)
References 597(14)
Index 611