This volume includes the best papers presented at the CHAOS 2008 International Conference on Chaotic Modeling, Simulation and Applications. It provides a valuable collection of new ideas, methods, and techniques in the field of nonlinear dynamics, chaos, fractals and their applications in general science and in engineering sciences. It touches on many fields such as chaos, dynamical systems, nonlinear systems, fractals and chaotic attractors. It also covers mechanics, hydrofluid dynamics, chaos in meteorology and cosmology, Hamiltonian and quantum chaos, chaos in biology and genetics, chaotic control, and chaos in economy and markets, and chaotic simulations; thus, containing cutting-edge interdisciplinary research with high-interest applications. These contributions present new solutions by analyzing the relevant data and through the use of recent advances in different fields, especially in chaotic simulation methods and techniques.
Author(s): Christos H. Skiadas, Loannis Dimotikalis, Charilaos Skiadas
Publisher: WS
Year: 2009
Language: English
Pages: 435
CONTENTS......Page 12
Preface......Page 6
International Advisory Committee......Page 8
Plenary and Keynote Talks......Page 10
1. Introduction......Page 18
2. System Description......Page 20
3. Mathematical Model......Page 21
4. System Response Without Damper Windings, AVR and PSS......Page 24
5. Addition of Damper Windings......Page 26
6. Addition of Damper Windings, AVR and PSS......Page 27
References......Page 30
2. The Samples......Page 31
3. Measurements and Simulation......Page 32
4.2. NNSD and SR determined from the experiment......Page 34
4.3. NNSD and SR determined from simulation......Page 35
References......Page 38
1. Introduction......Page 39
2. The Novel Friction Model......Page 40
3. The Analyzed System......Page 41
4. Computer Simulation Results......Page 42
5. Conclusions......Page 45
References......Page 47
1. Introduction......Page 48
2.2. Geometric phase from (an)holonomy......Page 50
2.3. The coupling parameter ......Page 51
2.4. The geometric feedback condition leading to chaotic precession......Page 52
2.5. Approaching the dynamics of MAP with Chua's Circuit......Page 53
3.1. Tschebysche polynomials of the rst kind......Page 55
3.2. MAP and relativity......Page 56
4. MAP Spin-Network Connection (Type III)......Page 57
5. Conclusions......Page 58
References......Page 59
1. Log-Periodic Oscillations......Page 60
2. Chaotic Behaviour......Page 61
3. Rescaled Range Analysis......Page 65
4. Conclusions......Page 66
References......Page 67
1. Introduction......Page 68
2. Toy Model......Page 69
3. Numerical Study and Preliminary Conclusions......Page 71
References......Page 73
1. The Dynamical Systems Approach to Large-Scale Mixing and Transport in the Ocean......Page 75
2. Cross-Frontal Chaotic Transport in a Kinematic Model of a Meandering Jet......Page 77
3. Cross-Frontal Chaotic Transport by Rossby Waves in a Dynamic Model of a Jet Current......Page 82
4. Conclusion......Page 84
References......Page 86
1. Introduction......Page 87
2.1. Design......Page 88
2.2. Experimental results and time-series analysis......Page 89
3.1. Lyapunov spectra and complexity calculations......Page 91
3.2. Phase dependence......Page 93
References......Page 94
1. Introduction......Page 96
2. Preliminaries on Fractional Calculus......Page 97
3. Variations of the Hermite Process......Page 99
4. Variations of the Rosenblatt Process......Page 101
5. Estimators for the Self-Similarity Index H......Page 102
References......Page 103
1. Introduction......Page 104
2. The Model......Page 105
3. Existence and Properties of Long Run Equilibria......Page 107
4. Bifurcation Analysis......Page 108
References......Page 111
1. Introduction......Page 113
2. Eigenvalues of Random Matrices......Page 115
3. Deviations......Page 117
4. Conclusion......Page 119
References......Page 120
1. Introduction......Page 121
2. Fractal Interpolation Functions in 1D......Page 122
3. Determination of the Vertical Scaling Factors......Page 124
4. Results......Page 126
5. Conclusions and Further Work......Page 127
References......Page 128
1. Introduction......Page 129
2.2. An example: The logistic map......Page 132
3.1. General remarks......Page 134
4. Conclusion......Page 136
References......Page 137
1. Introduction......Page 138
2. Finite Dimensional Approximation......Page 139
3. Analysis of the Bifurcations......Page 140
4. The Control Strategy......Page 143
References......Page 146
1. Introduction......Page 147
2. Asymptotic Expansion under Small ......Page 148
3. Asymptotic Expansion under Large ......Page 151
4. Conclusions......Page 153
References......Page 154
1. Introduction......Page 155
2. Wavelet-Chaos Methodology for EEG Sub-Band Analysis......Page 157
3. Classification Feature Space: Preliminary Results......Page 159
4. Classifier Design: Artificial Neural Networks......Page 161
References......Page 164
1. Introduction......Page 166
2. Discrete-Time Chaotic Additive Systems......Page 167
3. Input and Output Signal Quantization......Page 170
4. State Quantization Effects......Page 172
5. Conclusions......Page 173
References......Page 174
1. Introduction......Page 175
2. Methodology......Page 177
4. Solving the Selection Problem......Page 179
5. Concluding Comments......Page 181
References......Page 182
2. Complete Chaotic Maps......Page 183
3. A Unified Formulation......Page 186
References......Page 190
1. Introduction......Page 191
2. The Robot......Page 192
3. The experiment......Page 193
4. The Neural Network......Page 194
5. The Simulation......Page 195
References......Page 196
2. A `Cost' for Ignorance the Information Loss Law in the ONES......Page 197
3. Bene ts for the ONES......Page 200
4. Problems for the ONES......Page 203
5. Conclusions......Page 205
References......Page 206
1. Introduction......Page 207
2. Differential Equations for Physical Values Describing a Slow-Flowing Gravitational Compression under Unobservable Velocities of Particles......Page 208
3. Velocity of Autowave Front Propagation in a Slowly Gravitational Compressible Spheroidal Body......Page 210
References......Page 215
1. Introduction......Page 216
2. Dissipative Dynamical Maps......Page 217
4. Conclusions......Page 218
References......Page 220
1. Introduction......Page 221
2. Plasma and Measurement......Page 222
3.1. Lissajous figure......Page 224
3.2. Loading plots......Page 227
4. Discussion......Page 228
References......Page 230
Chaos and Multifractals in the Solar System Plasma W. M. Macek......Page 231
1. Importance of Chaos and Multifractality......Page 232
3. Solar Wind Data......Page 233
4.1. Generalized dimensions......Page 234
4.2. Turbulence scaling......Page 235
5.1. Dimensions for solar wind attractor and turbulence models......Page 236
5.2. Multifractal spectrum for turbulence......Page 237
6. Conclusions......Page 238
References......Page 239
1. Introduction......Page 241
2.3. Equilibria and their stability......Page 243
3.1. Lyapunov exponents......Page 244
3.2. Attractors of the hyperchaotic complex L u system......Page 245
3.2.3. Fix = 42; = 10; = 25 and vary ......Page 246
4. Conclusions......Page 247
References......Page 248
1. Introduction......Page 249
2. Chaotic Measures and Biological Signals......Page 250
3. Clinical Measurements......Page 251
4.1. Maximal Lyapunov Exponent (MLE)......Page 252
4.2. Correlation Dimension (CD)......Page 253
4.5. Relaxation Parameter (RP)......Page 254
4.6. Comparison of baseline deviation and measure sensitivity......Page 255
5. Discussion......Page 256
6. Conclusions......Page 257
References......Page 258
2. Method......Page 259
3. Applications......Page 263
4. Conclusions......Page 266
References......Page 267
1. Introduction......Page 268
2. Directional Coupling Measures......Page 269
2.1. State space measures......Page 270
2.2. Synchronization measures......Page 271
2.3. Information measures......Page 272
3. Setup......Page 274
4. Results......Page 275
5. Application......Page 278
References......Page 280
1. Introduction......Page 282
2. Creating Material with a Desired Refraction Coefficient......Page 284
3. A Discussion of the Recipe......Page 287
3.1. Negative refraction......Page 288
3.2. Wave-focusing property......Page 289
References......Page 290
1. Introduction......Page 291
2.1. Model systems......Page 292
2.3. Inducing phase correlations......Page 294
3. The IPAFT Algorithm......Page 295
4.1. Convergence......Page 296
4.2. Applications to the Lorenz system......Page 298
5. Conclusions......Page 301
References......Page 302
1. Introduction......Page 303
2. Literature Review......Page 304
3. The Structure of the Experimental Time Series......Page 305
4. Analysis of Chaotic Data......Page 306
5. Conclusions......Page 308
References......Page 310
1. Introduction......Page 311
2.1. Local aspect of the method......Page 313
3. Application of the Variation Method for the Fracture Surfaces......Page 314
References......Page 315
1. Introduction......Page 316
2. Dynamic Modeling of Nonliner Suspension......Page 317
3. Bifurcation of Nonlinear Suspension......Page 318
4.2. Numerical simulation......Page 321
6. Conclusions......Page 323
References......Page 324
2. Chaotic Modeling......Page 326
3. Chaotic Simulation......Page 328
References......Page 330
Quantum Chaos: Degree of Reversibility of Quantum Dynamics of Classically Chaotic Systems V. V. Sokolov et al.......Page 331
1. Introduction......Page 332
2. The Phase Space Approach......Page 333
3. Reversibility and Peres Fidelity......Page 335
4. Peres Fidelity and the Number of Harmonics......Page 336
5. Reversibility Versus the Number of Harmonics......Page 338
References......Page 339
1. Introduction......Page 340
2.1. Experiments......Page 342
2.2. Experimental results......Page 343
3.1. Random matrix model for coupled systems......Page 344
3.2. Independent transmit and receive channels......Page 345
3.3. Correlations on the transmit and receive side......Page 346
References......Page 347
1. Introduction......Page 348
2.2. Nonlinear components G(x)......Page 349
3.1. Use of nonlinear component G1(x)......Page 350
3.2. Use of nonlinear component G2(x)......Page 351
4.1. Two examples of CFOA-based Sprott's sinusoidal oscillators......Page 352
4.2. Two examples of CFOA-based Sprott's chaotic oscillators......Page 353
References......Page 354
1. Introduction......Page 355
2. The Coin Model......Page 356
3. Results and Discussion......Page 358
References......Page 360
1. Introduction......Page 361
2. Analytical Formulation......Page 362
3. The Investigated Containership......Page 364
4. Dynamic Analysis using the Continuation Method......Page 365
5. Conclusions......Page 368
References......Page 369
1. Introduction......Page 370
2. Synchronization using Pecora and Carroll Method......Page 371
3. Synchronization using Active Control......Page 373
4. Linear Generalized Synchronization of Genesio System......Page 375
5. Numerical Results......Page 377
References......Page 380
1. Motivation......Page 381
2. Physical Processes under Outbursts of Mountain WO and their Risk Assessments......Page 383
3. Break-Through Water Wave Propagation......Page 388
4. Assessment of Damages......Page 390
5. Conclusion......Page 392
References......Page 393
1. Introduction......Page 395
2. Univariate Embedding......Page 396
3. Multivariate Embedding......Page 397
4. Comparing Reconstructions......Page 399
5. Simulations and Results......Page 401
6. Conclusions......Page 403
References......Page 404
1. Introduction......Page 405
2. Recurrence Plots and Recurrence Analysis of Traffic Flow Dynamics......Page 406
3. Analysis of Urban Freeway Traffic Flow Dynamics using Recurrences......Page 408
4. Conclusions......Page 411
References......Page 413
1. Nonlinear Evolutionary System Identification......Page 415
2. Comparing Results of Evolutionary Modeling......Page 416
3. Empirical Tests......Page 420
4. Conclusion......Page 421
References......Page 422
1. Introduction......Page 423
2. Plasma Impurities......Page 424
3. The Plasma Sheath......Page 425
4.1. Preparation of samples-treatment of samples......Page 428
4.2. Results......Page 429
5. Conclusions......Page 430
References......Page 432
Author Index......Page 434
