Chaos Theory: Modeling, Simulation and Applications

Contents......Page 12
Preface......Page 6
International Scientific Committee......Page 8
Keynote Talks......Page 10
PART I Plenary and Keynote Papers......Page 17
1 Introduction......Page 19
2 Lagrangian approach in studying surface transport and mixing in the ocean......Page 20
3 MHI Japan Sea circulation model......Page 23
4 Results......Page 24
5 Conclusion......Page 28
References......Page 29
Nonlinearity of Earth: Astonishing diversity and wide prospects......Page 30
EXPERIMENTS......Page 34
ANALYTICAL TREATMENT......Page 35
REFERENCES......Page 36
1 Introduction......Page 37
2 Informative example. How to make a weather forecast for a week. The reason why it cannot be made for more than two weeks......Page 38
4 The Klausewitz principle......Page 40
5 The Klausewitz principle in the problems with bounded resources......Page 42
6 The "master-slave" principle......Page 43
8 The principle of wide latitude......Page 44
References......Page 45
1 Introduction......Page 46
2 Brownian motion......Page 47
3 Stochastic differential equations......Page 49
4 Markov property......Page 51
5 The probability of extinction of a genotype......Page 52
References......Page 56
1 Introduction......Page 57
2 Creating material with a desired refraction coefficient by embedding small inhomogeneities into a given material......Page 59
3 A discussion of two recipes......Page 64
3.1 Negative refraction......Page 65
3.2 Wave-focusing property......Page 66
References......Page 67
1. Introduction......Page 69
2. The Model and Simulations......Page 70
References......Page 74
Classical versus quantum dynamical chaos: Sensitivity to external perturbations, stability and reversibility......Page 75
1 Introduction......Page 76
2 The model......Page 79
3.1 Coarse-graining and mean values......Page 81
3.2 The information entropy......Page 83
4.1 Weak noise limit......Page 84
4.2 Strong noise limit......Page 87
5 Reversibility: von Neumann entropy and purity......Page 89
6 Summary......Page 91
References......Page 92
1. Introduction......Page 93
2. The upper limit of the parameter r......Page 94
3. The existence of fixed points......Page 95
4. The stability of fixed points......Page 96
5. The solution of the fixed points equation......Page 98
6. Approximate fixed points......Page 99
References......Page 101
PART II Invited and Contributed Papers......Page 103
1 Introduction......Page 105
2 Stochastic model of developed turbulence......Page 107
3 Calculation of the Kolmogorov constant and skewness factor......Page 110
4 Conclusion......Page 111
References......Page 112
1. Introduction......Page 113
2. The Model......Page 114
3. Method......Page 116
4. Results......Page 117
5. Discussion and Conclusion......Page 119
References......Page 120
2. Modelling of composite with cellular automata......Page 121
3. Numerical simulations......Page 122
4. Fractal characteristics of defects growth......Page 124
References......Page 125
1 Introduction......Page 126
2 Flow Decomposition in Dissipative Systems: R2 versus R3......Page 127
3 The Lorenz Attractor from Dissipative Dynamics of Intersecting Quadratic Surfaces......Page 130
4 The Rössler Attractor from Dissipative Dynamics of a Cylinder Intersecting with an Helicoid......Page 133
References......Page 135
1. Introduction......Page 136
2. A Lienard System......Page 138
3. Advantage Over Linear Stability Analysis......Page 141
References......Page 142
1. Introduction: The Fractal Market Hypothesis......Page 143
2. Time Series Analysis......Page 144
3. Conclusion......Page 148
References......Page 149
1. Introduction......Page 151
2.1. Coupling two unimodal piecewise linear maps......Page 152
2.2. Coupling two bimodal piecewise linear maps......Page 154
3. Duffing Application......Page 155
5. Conclusions......Page 157
References......Page 158
1. Introduction......Page 159
2.1. Scheme of the proposed enciphering method......Page 161
3. Analyze of results of the proposed enciphering algorithm......Page 164
3.2. Results when enciphering images......Page 165
References......Page 166
Introduction......Page 167
Model maps......Page 168
Reinjection Probability Distribution......Page 170
The effect of the Noise on the RPD......Page 172
Acknowledgements......Page 173
References......Page 174
1. Introduction......Page 175
3. Multifractality and wavelet transform......Page 176
5. Estimated parameters and statistical analysis......Page 178
6. Results and discussion......Page 179
References......Page 182
1. Introduction......Page 183
2.1. White tune......Page 184
2.2. Brown tune......Page 185
2.3. Pink tune......Page 186
2.4. L systems in music......Page 187
3. Curve aesthetics......Page 188
References......Page 189
Time variant chaos encryption......Page 191
1. Introduction......Page 192
2. The Analog Modulation Case......Page 193
3. The Discrete-Time Case......Page 195
4. Conclusions......Page 197
References......Page 198
1. Introduction......Page 199
2. What is Algorithmic and Generative Composition?......Page 200
3. What is “Successful”?......Page 201
3.1. Human Intervention......Page 202
3.2. Complexity of Mapping......Page 203
3.3. The Importance of Timbre......Page 204
4. Conclusion......Page 205
5. References......Page 206
1. Introduction......Page 207
2.2. Mean-motion resonance......Page 208
4. The Simulated Data......Page 209
5.3. Choice of local AMI minimum time delay optimizes baseline noise reduction......Page 211
6. Conclusions......Page 213
Acknowledgement......Page 214
1. Introduction......Page 215
2. Perturbative analysis in spectral domain......Page 216
3.1. Quintic nonlinearity......Page 217
3.2. Higher-order dispersions......Page 218
3.3. Narrowband losses: A gas filled oscillator or an impured fiber......Page 220
4. Conclusions......Page 221
References......Page 222
1. Introduction......Page 223
2. Problem Statement......Page 224
3. Proposed Modified CSK Method......Page 225
4. Implementation using Lorenz and Chua’s System......Page 226
5. Security Analysis......Page 227
References......Page 229
1 Introduction......Page 231
2 Cauchy-Kowalevski Theorem......Page 232
3 Observer’s Mathematics Arithmetic and Derivatives......Page 233
5 Schrodinger Equation......Page 235
6 Two-Slit Interference......Page 236
8 Acknowledgments......Page 237
References......Page 238
1. Introduction......Page 239
2.1. Humanities versus Natural Sciences......Page 240
2.2. The four causes of Aristotle......Page 241
3. Musical application......Page 242
References......Page 246
1. Generalization involving xky Coupling......Page 247
2. Time Series Analysis......Page 249
3. Bifurcation Analysis......Page 252
4. Conclusion......Page 253
References......Page 254
1. Introduction......Page 255
2.1. The CCRF-CEM cell line......Page 256
2.4. Mathematical model and analysis......Page 257
3. Results......Page 258
4. Conclusion......Page 260
References......Page 262
1. Introduction......Page 263
2. Fractality and Scale Invariance......Page 264
3. Detrended Fluctuation Analysis (DFA)......Page 265
4. Classical Case: Map Module 1......Page 266
5. Quantum Case: Nuclear spectra......Page 268
References......Page 270
1. Introduction......Page 271
2. Measurement methodology......Page 272
2.1. Electrical measurements......Page 273
3. Acoustic measurements and deconvolution......Page 274
4. Discussion......Page 278
6. References......Page 279
1. Introduction......Page 281
2. Experiment......Page 282
3. The enhancement factor......Page 283
4. The properties of the directed microwave networks......Page 286
5. Summary......Page 287
References......Page 288
1. Introduction......Page 289
3.1 Hodge Podge Machine......Page 291
4. Simultaneous Behaviours......Page 293
5. Adding Dynamism......Page 294
References......Page 296
1. Introduction......Page 297
2.2. Conventional large-scale forcing......Page 299
2.3. Reduced-communication forcing (RCF)......Page 300
3.1. Steady isotropic turbulence......Page 301
3.2. Parallel computing for higher Reynolds numbers......Page 302
Acknowledgments......Page 303
References......Page 304
1 Introduction......Page 305
2 Information causality measures and proposed corrections......Page 306
3 Results......Page 308
4 Discussion......Page 311
References......Page 312
1. Introduction......Page 313
3. Complexity as a kind of macroscopic quanticity......Page 314
4. Quantum theory as a kind of microscopic chaoticity or complexity......Page 315
6. Mathematical traces of complexity theory......Page 316
6.2 The dynamical point of view......Page 317
6.3 Fractal theory space and renormalization group theory......Page 318
6.4 Scale Relativity Theory......Page 319
7. Becoming before Being......Page 320
8. Chaos, fractals and unification of dynamics to thermodynamics......Page 321
9. Epilogue: Complexity theory and unification of cosmos......Page 322
References......Page 323
1. Introduction......Page 325
2. An extension of the Beta densities, and Gompertz growth model......Page 327
3. Dynamical study of the models proportional to Beta*(p,q) densities — a brief sketch......Page 328
4. Beta*(p,q) models as signed mixtures of power functions......Page 331
References......Page 332
1. Introduction......Page 333
2.1. Basic operation principles of buck converter......Page 334
2.2. Switched state-space (SSS) model......Page 335
2.3. Power System Blockset (PSB) model......Page 336
2.4. The model based on iterative mappings......Page 337
3. Simulation Results......Page 338
4. Conclusions......Page 339
References......Page 340
Chaos as compositional order......Page 341
1. The composer-performer balance......Page 342
2. Arnold tongues and tuning systems......Page 344
3. Music for voices – Circles 7......Page 345
4. Conclusion......Page 347
References......Page 348
Beta(p,q)-Cantor sets: Determinism and randomness......Page 349
2. Random and deterministic Beta(p,q)-Cantor sets......Page 350
3. The Hausdorff dimension of the random and deterministic Beta(p,q)-Cantor sets......Page 352
4. Numerical simulations......Page 354
References......Page 356
1. Introduction......Page 357
2. Lyapunov exponents and direct (second) method......Page 358
3.1. Single-well cubic potential......Page 360
3.2. Mathematical pendulum......Page 361
3.3. Two coupled oscillators......Page 362
4. Conclusions......Page 363
References......Page 364
1. Introduction......Page 365
2.1. Duffing oscillator under two-frequency excitation......Page 366
2.2. Averaged equations......Page 367
3.1. Homoclinic bifurcation condition......Page 369
3.2. Melnikov criterion and averaging......Page 371
References......Page 372
Introduction......Page 373
The Stochastic Modeling......Page 374
Properties of the Stochastic Model......Page 375
Projection to 2050 of mortality for females in Sweden......Page 379
Summary and Conclusions......Page 383
References......Page 384
1. Introduction......Page 385
2. The mathematical chaotic pitches......Page 387
3. The musical pitches......Page 389
4. The musical scores......Page 391
5. Conclusions......Page 393
6. References......Page 394
1. Introduction......Page 395
2. The sound generating maps......Page 397
3. The sound’s energy......Page 398
4. The sound’s overtones......Page 399
5. The sound’s phase......Page 400
6. Effect of initial loudness......Page 401
7. References......Page 402
1. Introduction......Page 404
2. The rainbow musical scale......Page 406
3. Mapping the mathematical pitch onto the rainbow musical scale......Page 407
5. The elliptic chaotic model......Page 408
6. Fully chaotic pitches and durations......Page 410
7. The musical scores......Page 412
8. References......Page 413
1. Introduction......Page 415
2. A One-Parameter Highly Chaotic Attractor......Page 416
3.2. A Dual-Channel Single-Attractor Receiver......Page 418
3.3. Numerical Results......Page 419
3.4. An Alternative Dual-Channel Single-Attractor Receiver......Page 420
References......Page 421
1. Introduction......Page 422
2. Geometric collective model......Page 423
3. Interacting boson model......Page 427
4. Conclusions......Page 428
References......Page 429
1. Introduction......Page 430
2. Computational model of Collective Intelligence......Page 431
3. Importance of Chaos in Collective Intelligence systems......Page 437
References......Page 438
1. Introduction......Page 439
2. The basic circuit and its equivalent scheme......Page 440
4.2. Measuring results......Page 443
5. Conclusions......Page 445
References......Page 446
1. Introduction......Page 447
2.1. Set-up description......Page 448
2.2. Experimental results......Page 449
3. Theoretical model......Page 452
References......Page 454
2. Methods......Page 455
3. Results......Page 457
4. Discussion......Page 459
References......Page 460
2. Experimental Procedure and Results......Page 461
References......Page 464
Author Index......Page 465