Chaotic Systems: Theory and Applications, Selected Papers from the 2nd Chaotic Modeling and Simulation International Conference (CHAOS2009)

Contents......Page 10
Preface......Page 6
Honorary Committee and International Scientific Committee......Page 7
Keynote Talks......Page 9
1. Introduction......Page 14
2. System Description......Page 15
4. System Response in Case of Absence of Saturation......Page 16
5. System Response in Presence of Saturation......Page 19
Conclusions......Page 20
References......Page 21
1 Introduction......Page 22
3 Lyapunov stability and Lyapunov exponent......Page 23
4 Multiplicative logistic equation X2n = rx1 - x......Page 24
5 Multiplicative Lorenz system......Page 26
References......Page 28
1. Introduction......Page 30
2. Experimental setup......Page 31
3. Mathematical model......Page 32
4. Parameter estimation and experimental vs. numerical results......Page 35
References......Page 38
1 Introduction......Page 40
2 EnKF as a mean-field process......Page 41
3 Particle filters regimes......Page 42
5 The filtering of atmospheric turbulent wind with Local Particle Filter......Page 44
6 Outcomes and further developments......Page 46
References......Page 47
1 Introduction......Page 48
2 Order-chaos-order transitions......Page 49
3 Approximated piecewise Jacobian......Page 50
4 Jacobian-based local Lyapunov exponents......Page 51
5 Reasons for local < 0 in chaos......Page 52
6 Global Lyapunov exponents......Page 53
7 Conclusions......Page 54
Bibliography......Page 55
1 Introduction......Page 56
2 The model......Page 57
3 Results......Page 60
References......Page 63
1. Introduction......Page 64
2.1. The original model, set up and starting materials......Page 65
2.2. Our set up and experimental end-member compositions......Page 67
3. Sample Preparation and Preliminary Electron Microprobe (EMP) Data......Page 68
4. Conclusions......Page 70
References......Page 71
1 Introduction......Page 72
2 The model......Page 73
3 Fixed points and their stability......Page 74
4 Local and global bifurcation analysis......Page 76
References......Page 79
1 Introduction......Page 80
2 The mathematical model with discrete time and consumer sentiment......Page 81
3 The dynamic behavior of the model (6)......Page 82
4 The normal form for flip and Neimark-Sacker bifurcations......Page 83
6 Numerical simulation......Page 86
References......Page 87
1 Introduction......Page 88
2 Gamma entropy flows......Page 90
3 Constrained degeneration of order......Page 91
4 Bivariate gamma processes......Page 92
5 Weibull processes......Page 95
References......Page 97
1. Introduction......Page 98
2. General Results......Page 99
3.1. The Lorenz system......Page 101
3.2. The modified Chen system......Page 103
References......Page 105
1 Introduction......Page 106
2.1 Trivial subsidary condition decoupling......Page 108
2.2 Trivial subsidiary condition decoupling P......Page 109
4 Possibility of oscillatory solutions......Page 110
5 Periodic Analysis of Maxwell Bloch Model......Page 111
7 Conclusion......Page 112
References......Page 113
1 Introduction......Page 114
2.2 Locally projective nonlinear noise reduction......Page 115
3 Analysis of Measured Data......Page 116
3.1 Phase-space analysis of PG 1351+489 light curve......Page 117
5 Comparison of Model and Measured Data......Page 118
6 The Effect of "Resetting" on the PSRT......Page 119
7 The Three-Dimensional PSR-Frequency Spectrum......Page 120
9.1 Poincare plane orientation......Page 121
11 Acknowledgements......Page 122
References......Page 123
1 Introduction......Page 124
2 Arithmetic......Page 125
3 Derivatives......Page 126
5 Newton equation with chaos theory interpretation......Page 128
7 Lorentz transform with chaos theory interpretation......Page 129
References......Page 131
Introduction......Page 132
1. Unified Van-der-Paul/Rayleigh/Duffing Generator......Page 134
2. Unified Poincare Generator......Page 137
References......Page 140
Keywords:......Page 141
References......Page 146
1. Object model......Page 147
2. Modification of control laws......Page 148
Conclusion......Page 150
References......Page 151
2. Problem statement......Page 152
3. Numerical results......Page 155
References......Page 158
I. Introduction......Page 160
2. Multivariate analysis software......Page 161
Acoustic:......Page 162
PCA results:......Page 164
NPCA results:......Page 165
4. Conclusion......Page 166
References......Page 167
1. Introduction......Page 168
2. Chaos Shift Keying Communication......Page 169
3. Single-User CSK: Likelihood Decoding......Page 170
4. Single-User CSK: Exact and Approximate Bit Error Rate......Page 171
5. Multi-User CSK: Coherent and Non-Coherent......Page 173
References......Page 176
1. Introduction......Page 178
2. Bouncing ball......Page 179
References......Page 181
1. Introduction......Page 183
2. Rayleigh-Benard convective system......Page 184
3. Symmetries of the extended Lorenz system......Page 185
4. Statistical properties of the system - symmetric case......Page 187
5. Symmetry-break and phase mixing......Page 189
6. Symmetry-break and hyperbolicity......Page 190
7. Symmetry-break and low-frequency variability......Page 192
8. Summary and Conciusions......Page 194
Bibliography......Page 197
1 Introduction......Page 198
2 Results......Page 199
3 Interpretation and discussion......Page 200
References......Page 203
Keywords:......Page 204
1 Introduction......Page 205
2 Microwave cavities and ballistic quantum dots......Page 206
3 The scattering problem......Page 208
4 Doing statistics with the scattering matrix......Page 209
5 The maximum-entropy model......Page 210
6 Comparison of the information-theoretic model with numerical simulations......Page 212
6.1 Discussion......Page 216
7 Conclusions......Page 217
References......Page 219
2 Formulation of the problem......Page 220
3 Long-wavelength linear stability analysis......Page 222
References......Page 227
1 Introduction......Page 228
2.2 Parametric Space......Page 229
4 Symmetry Broken and Chaos......Page 230
4.2 Normalized Phase factor ( parameter: exp(gi(z)))......Page 232
5 Remark......Page 235
References......Page 236
1.1 Transition probabilities......Page 237
2 Markov property......Page 240
2.2 The strong Markov property......Page 241
3 Application......Page 243
References......Page 244
1. Introduction......Page 245
2. The classical HM......Page 246
3. Phase space structure of the HM......Page 247
4. The manifold of LFPs......Page 249
5. Stability of LFPs......Page 250
References......Page 252
1. Introduction......Page 254
2. Spherical expansion of the Beltrami equation......Page 255
3. The Transmission Line model......Page 256
4. Trapped modes and bound states......Page 257
5. Beltrami solutions through the Lorentz group......Page 259
References......Page 260
Appendix I......Page 261
1 Single-user coherent CSK: The model......Page 262
3 Family of deformed circular maps......Page 263
4 Paired Bernoulli circular spreading (PBCS)......Page 266
5 Single-user non-coherent CSK: The model......Page 267
6 Monte Carlo Maximum Likelihood Decoding......Page 268
References......Page 269
1. Introduction......Page 270
2. The q-deformation of nonlinear maps......Page 271
2.2. The q-deformed Henon map......Page 272
3. Results and Discussion......Page 273
4. Conclusions......Page 279
References......Page 280
1. Introduction......Page 281
2. Far from Equilibrium Physical Processes......Page 282
2.1. The modern unified theory of the far from equilibrium physical processes......Page 283
3.1. Solar flares......Page 284
3.2. Magnetosphere......Page 286
3.3. Earthquakes......Page 287
3.3. Human brain and cardiac rhythm......Page 289
4. Summary of Data Analysis and Results......Page 291
5.1. Critical points and spinodal nucleation......Page 292
5.2. Local structures, turbulence, intermittency, anomalous diffusion and synchronization in extended systems......Page 293
References......Page 295
1 Introduction......Page 297
2 Limitations of the Current Schemes......Page 298
3.1 The Topology of the L-AdNN......Page 299
3.2 The Weights of the L-AdNN: Gradient Search......Page 300
4 Lyapunov Exponents Analysis of the L-AdNN......Page 301
5.1 Comparative Chaotic Properties......Page 303
5.2 Comparative PR Properties......Page 304
6 Conclusions......Page 305
References......Page 306
1 Introduction - Setup......Page 307
2 Attracting invariant manifolds for inertial particles......Page 309
3 Application to the ABC flow......Page 311
References......Page 314
1. Introduction......Page 315
2. The Model and Simulations......Page 316
References......Page 321
1 Introduction......Page 322
2.1 Fragmentation of the resonance states because of the influence of the background......Page 323
3.1 Isolated doorway resonance......Page 325
3.2 Overlapping doorway resonances......Page 327
4 Ensemble averaging......Page 329
References......Page 332
1. Introduction......Page 333
2. The model......Page 334
3. Analysis, numerical results, and discussion......Page 335
References......Page 339
1. Introduction......Page 340
2. The model......Page 341
3. Analysis......Page 342
4. Numerical Results and Chaotic Compositions......Page 344
References......Page 349
1. Introduction......Page 351
2. A Fractional Integrator......Page 352
4. Numerical Results......Page 354
References......Page 356
1 Introduction......Page 359
2 Fuzzy system description using rule firing indicator functions and HONNF......Page 361
3.1 Problem formulation and neuro-fuzzy representation......Page 362
3.2 Adaptive regulation with modeling error effects......Page 365
4.1 Inverted pendulum......Page 368
4.2 Van der pol......Page 369
5 Conclusions......Page 371
References......Page 372
2 Fundamental concepts......Page 375
3 NSG system......Page 377
4 Cartwright's method......Page 378
References......Page 381
1 Introduction......Page 382
2 Atomic wave-packet motion in a laser standing wave......Page 383
3 Quantum-classical correspondence......Page 388
References......Page 389
1. Introduction......Page 390
2. New experimental results......Page 391
3. Previous results......Page 394
4. Summation-elaboration tables......Page 395
References......Page 397
1. Introduction......Page 398
2.1. Acid-Infiltration Experiments......Page 400
2.2. Preliminary Tests......Page 401
2.3. Composition Analysis of the Treated Rock......Page 402
3.1. Stage I......Page 403
3.2 Stage II......Page 404
5. Conculsions......Page 405
References......Page 406
Author Index......Page 408