| 1. Necessity for a Science of Complex Systems 1.1 Introduction 1.2 Chaos 1.3 Chaos and Complexity 1.4 How Has Chaos Changed Our Way of Thinking? 1.4.1 Dialectic Method to Overcome the Antithesis Between Determinism and Nondeterminism or Between Programs and Errors 1.4.2 Dialectic Method to Overcome the Antithesis Between Order and Randomness 1.4.3 Beyond the Antithesis Between Reductionism and Holism 1.5 Dynamic Many-to-Many Relations and Bio-networks 1.5.1 The Necessity of Dynamic Many-to-Many Relations . 1.5.2 Metabolic Systems, Differentiation, and Development 1.5.3 Ecosystems 1.5.4 Immune Systems 1.5.5 The Brain 1.5.6 Rugged Landscapes and Their Problems 1.5.7 Conclusion 1.6 The Construction of an Artificial (Virtual) World 1.7 A Trigger to Emergence 1.8 Beyond Top-Down Versus Bottom-Up 1.9 Methodology of Study of Complex Systems 1.9.1 Constructive Way of Understanding 1.9.2 Plural Views 1.9.3 Mathematical Anatomy 1.9.4 The Problem of Internal Observers 2. Observation Problems from an Information-Theoretical Viewpoint 2.1 Observation Problems of Chaos 2.2 Undecidability and Entire Description 2.3 A Demon in Chaos 2.4 Chaos in the BZ Reaction 2.5 Noise-Induced Order 2.6 Could Structural Stability Lead to an Adequate Notion of a Model? 2.7 Information Theory of Chaos 3. CMLs: Constructive Approach to Spatiotemporal Chaos 3.1 From a Descriptive to a Constructive Approach of Nature 3.2 Coupled Map Lattice Approach to Spatiotemporal Chaos 3.2.1 Spatiotemporal Chaos 3.2.2 Introduction to Coupled Map Lattices 3.2.3 Comparison with Other Approaches 3.3 Phenomenology of Spatiotemporal Chaos in the Diffusively Coupled Logistic Lattice 3.3.1 Introduction 3.3.2 Frozen Random Patterns and Spatial Bifurcations 3.3.3 Pattern Selection with Suppression of Chaos 3.3.4 Brownian Motion of Chaotic Defects and Defect Turbulence 3.3.5 Spatiotemporal Intermitteney (STI) 3.3.6 Stability of Fully Developed Spatiotemporal Chaos (FDSTC) Sustained by the Supertransients 3.3.7 Traveling Waves 3.3.8 Supertransients 3.4 CML Phenomenology as a Problem of Complex Systems 3.5 Phenonemology in Open-Flow Lattices 3.5.1 Introduction 3.5.2 Spatial Bifurcation to Down-Flow 3.5.3 Convective Instability and Spatial Amplification of Fluctuations 3.5.4 Phase Diagram 3.5.5 Spatial Chaos 3.5.6 Selective Amplification of Input 3.6 Universality 3.7 Theory for Spatiotemporal Chaos 3.8 Applications of Coupled Map Lattices 3.8.1 Pattern Formation (Spinodal Decomposition) 3.8.2 Crystal Growth and Boiling 3.8.3 Convection 3.8.4 Spiral and Traveling Waves in Excitable Media 3.8.5 Cloud Dynamics and Geophysics …… 4 Networks of Chaotic Elements 5 Significance of Coupled Chaotic Systems 6 Chaotic Information Processing in the Brain 7 Conversations with Authors References Index |
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