Contents -- Preface -- Honorary Committee -- International Scientific Committee -- Keynote Talks -- PART I Plenary and Keynote Papers -- Lagrangian approach to chaotic transport and mixing in the Japan Sea -- 1 Introduction -- 2 Lagrangian approach in studying surface transport and mixing in the ocean -- 3 MHI Japan Sea circulation model -- 4 Results -- 5 Conclusion -- References -- Nonlinearity of Earth: Astonishing diversity and wide prospects -- INTRODUCTION -- EXPERIMENTS -- ANALYTICAL TREATMENT -- CONCLUSIONS -- REFERENCES -- Dynamic principles of prognosis and control -- 1 Introduction -- 2 Informative example. How to make a weather forecast for a week. The reason why it cannot be made for more than two weeks -- 3 Prognosis of market behavior as the analog of weather forecast -- 4 The Klausewitz principle -- 5 The Klausewitz principle in the problems with bounded resources -- 6 The "master-slave" principle -- 7 The principle of continuous successful process -- 8 The principle of wide latitude -- 9 The Thermidor Law -- References -- On a problem of approximation of Markov chains by a solution of a stochastic differential equation -- 1 Introduction -- 2 Brownian motion -- 3 Stochastic differential equations -- 4 Markov property -- 5 The probability of extinction of a genotype -- References -- Scattering by many small inhomogeneities and applications -- 1 Introduction -- 2 Creating material with a desired refraction coefficient by embedding small inhomogeneities into a given material -- 3 A discussion of two recipes -- 3.1 Negative refraction -- 3.2 Wave-focusing property -- References -- Modeling recent economic debates -- 1. Introduction -- 2. The Model and Simulations -- 3. Conclusions -- References -- Classical versus quantum dynamical chaos: Sensitivity to external perturbations, stability and reversibility -- 1 Introduction.

2 The model -- 3 Coarse-grained features of quantum evolution -- 3.1 Coarse-graining and mean values -- 3.2 The information entropy -- 4 Sensitivity of quantum evolution to the noise -- 4.1 Weak noise limit -- 4.2 Strong noise limit -- 4.3 Moderate noise: scaling properties -- 5 Reversibility: von Neumann entropy and purity -- 6 Summary -- References -- On logistic-like iterative maps -- 1. Introduction -- 2. The upper limit of the parameter r -- 3. The existence of fixed points -- 4. The stability of fixed points -- 5. The solution of the fixed points equation -- 6. Approximate fixed points -- References -- PART II Invited and Contributed Papers -- Improved ε expansion in theory of turbulence: Calculation of Kolmogorov constant and skewness factor -- 1 Introduction -- 2 Stochastic model of developed turbulence -- 3 Calculation of the Kolmogorov constant and skewness factor -- 4 Conclusion -- Acknowledgments -- References -- Dynamics of a rubbing Jeffcott rotor with three blades -- 1. Introduction -- 2. The Model -- 3. Method -- 4. Results -- 5. Discussion and Conclusion -- 6. Acknowledgement -- References -- Exploring process of fibre breaking in tube samples of composite during quasi-static process of fracture -- 1. Introduction -- 2. Modelling of composite with cellular automata -- 3. Numerical simulations -- 4. Fractal characteristics of defects growth -- 5. Discussion -- 6. Acknowledgements -- References -- Non Hamiltonian chaos from Nambu dynamics of surfaces -- 1 Introduction -- 2 Flow Decomposition in Dissipative Systems: R2 versus R3 -- 3 The Lorenz Attractor from Dissipative Dynamics of Intersecting Quadratic Surfaces -- 4 The Rössler Attractor from Dissipative Dynamics of a Cylinder Intersecting with an Helicoid -- 5 Conclusions-Open Problems -- References -- A methodology for classifying periodic orbits -- 1. Introduction.

2. A Lienard System -- 3. Advantage Over Linear Stability Analysis -- 4. Conclusions -- Acknowledgements -- References -- Chaoticity in the time evolution of foreign currency exchange rates in Turkey -- 1. Introduction: The Fractal Market Hypothesis -- 2. Time Series Analysis -- 3. Conclusion -- References -- Symbolic dynamics and chaotic synchronization -- 1. Introduction -- 2. The Synchronization Problem -- 2.1. Coupling two unimodal piecewise linear maps -- 2.2. Coupling two bimodal piecewise linear maps -- 3. Duffing Application -- 4. Symbolic Dynamics -- 5. Conclusions -- References -- New enciphering algorithm based on chaotic generalized Hénon map -- 1. Introduction -- 2. The proposed enciphering method -- 2.1. Scheme of the proposed enciphering method -- 2.2. Deciphering -- 3. Analyze of results of the proposed enciphering algorithm -- 3.1. Results of encryption of natural language text -- 3.2. Results when enciphering images -- 4. Conclusions -- 5. Acknowledgement -- References -- Noise influence on the characteristic relations and reinjection probability densities of type-II and type-III intermittencies -- Introduction -- Model maps -- Reinjection Probability Distribution -- The effect of the Noise on the RPD -- Conclusions and Discussion -- Acknowledgements -- References -- Multifractal and wavelet analysis of epileptic seizures -- 1. Introduction -- 2. Experimental procedure -- 3. Multifractality and wavelet transform -- 4. Algorithm of the wavelet-transform modulus maxima (WTMM) method -- 5. Estimated parameters and statistical analysis -- 6. Results and discussion -- 7. Conclusions -- References -- Fractal based curves in musical creativity: A critical annotation -- 1. Introduction -- 2. Fractal curve methods -- 2.1. White tune -- 2.2. Brown tune -- 2.3. Pink tune -- 2.4. L systems in music -- 3. Curve aesthetics -- References.

Time variant chaos encryption -- 1. Introduction -- 2. The Analog Modulation Case -- 3. The Discrete-Time Case -- 4. Conclusions -- References -- Aesthetic considerations in algorithmic and generative composition -- 1. Introduction -- 2. What is Algorithmic and Generative Composition? -- 3. What is "Successful"? -- 3.1. Human Intervention -- 3.2. Complexity of Mapping -- 3.3. The Importance of Timbre -- 4. Conclusion -- 5. References -- Optimizing nonlinear projective noise reduction for the detection of planets in mean-motion resonances in transit light curves -- 1. Introduction -- 2. Transit Method for Detecting Mean-Motion Resonances -- 2.1. The transit method for detecting extrasolar planets -- 2.2. Mean-motion resonance -- 3. The Methodology -- 3.1. Phase-space portrait -- 3.2. Parameters of the reconstruction -- 3.3. Locally-projective nonlinear noise reduction -- 4. The Simulated Data -- 5. Results -- 5.1. Average mutual information -- 5.2. Choice of global-minimum delay optimizes noise reduction at maximum transit depth -- 5.3. Choice of local AMI minimum time delay optimizes baseline noise reduction -- 5.4. Comparison of optimization -- 6. Conclusions -- References -- Acknowledgement -- Dissipative solitons: Perturbations and chaos formation -- 1. Introduction -- 2. Perturbative analysis in spectral domain -- 3. Perturbations of CDS -- 3.1. Quintic nonlinearity -- 3.2. Higher-order dispersions -- 3.3. Narrowband losses: A gas filled oscillator or an impured fiber -- 4. Conclusions -- Acknowledgements -- References -- Modified chaotic shift keying using indirect coupled chaotic synchronization for secure digital communication -- 1. Introduction -- 2. Problem Statement -- 3. Proposed Modified CSK Method -- 4. Implementation using Lorenz and Chua's System -- 5. Security Analysis -- 6. Conclusions -- References.

Chaos problems in observer's mathematics -- 1 Introduction -- 2 Cauchy-Kowalevski Theorem -- 3 Observer's Mathematics Arithmetic and Derivatives -- 4 Free Wave Equation -- 5 Schrodinger Equation -- 6 Two-Slit Interference -- 7 Airy and Korteweg-de Vries Equations -- 8 Acknowledgments -- References -- Freedom and necessity in computer aided composition: A thinking framework and its application -- 1. Introduction -- 2. From Aristotle to evolutionary epistemology -- 2.1. Humanities versus Natural Sciences -- 2.2. The four causes of Aristotle -- 3. Musical application -- 4. Conclusions -- References -- A predator-prey model with the nonlinear self interaction coupling xky -- 1. Generalization involving xky Coupling -- 2. Time Series Analysis -- 3. Bifurcation Analysis -- 4. Conclusion -- References -- Evidence for deterministic chaos in aperiodic oscillations of acute lymphoblastic leukemia cells in long-term culture -- 1. Introduction -- 2. Materials and Methods -- 2.1. The CCRF-CEM cell line -- 2.2. Cell culture conditions -- 2.3. Measurements, experimental setup and model -- 2.4. Mathematical model and analysis -- 3. Results -- 4. Conclusion -- References -- Scale invariance in chaotic time series: Classical and quantum examples -- 1. Introduction -- 2. Fractality and Scale Invariance -- 3. Detrended Fluctuation Analysis (DFA) -- 4. Classical Case: Map Module 1 -- 5. Quantum Case: Nuclear spectra -- 6. Conclusions -- References -- Acoustic emission within an atmospheric helium discharge jet -- 1. Introduction -- 2. Measurement methodology -- 2.1. Electrical measurements -- 3. Acoustic measurements and deconvolution -- 4. Discussion -- 5. Acknowledgements -- 6. References -- Experimental investigation of the enhancement factor for irregular undirected and directed microwave graphs -- 1. Introduction -- 2. Experiment -- 3. The enhancement factor.

4. The properties of the directed microwave networks.