Complex systems : chaos and beyond : a constructive approach with applications in life sciences
著者
書誌事項
Complex systems : chaos and beyond : a constructive approach with applications in life sciences
Springer, c2001
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This book, the first in a series on this subject, is the outcome of many years of efforts to give a new all-encompassing approach to complex systems in nature based on chaos theory. While maintaining a high level of rigor, the authors avoid an overly complicated mathematical apparatus, making the book accessible to a wider interdisciplinary readership.
目次
- 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 Intermittency (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 Phenomenology 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.- 3.8.6 Ecological Systems.- 3.8.7 Evolution.- 3.8.8 Closing Remarks.- 4. Networks of Chaotic Elements.- 4.1 GCM Model.- 4.2 Clustering.- 4.3 Phase Transitions Between Clustering States.- 4.4 Ordered Phase and Cluster Bifurcation.- 4.5 Hierarchical Clustering and Chaotic Itinerancy.- 4.5.1 Partition Complexity.- 4.5.2 Hierarchical Clustering.- 4.5.3 Hierarchical Dynamics.- 4.5.4 Chaotic Itinerancy.- 4.6 Marginal Stability and Information Cascade.- 4.6.1 Marginal Stability.- 4.6.2 Information Cascade.- 4.7 Collective Dynamics.- 4.7.1 Remnant Mean-Field Fluctuation.- 4.7.2 Hidden Coherence.- 4.7.3 Instability of the Fixed Point of the Perron-Frobenius Operator.- 4.7.4 Destruction of Hidden Coherence by Noise and Anomalous Fluctuations.- 4.7.5 Heterogeneous Systems.- 4.7.6 Significance of Collective Dynamics.- 4.8 Universality and Nonuniversality.- 4.8.1 Universality of Clustering and Other Transitions.- 4.8.2 Globally Coupled Tent Map: Novelty Within Universality.- 5. Signifieanee of Coupled Chaotic Systems to Biological Networks.- 5.1 Relevance of Coupled Maps to Biological Information Processing.- 5.2 Application of Coupled Maps to Information Processing.- 5.2.1 Memory to Attractor Mapping and the Switching Process.- 5.2.2 Chaotic Itinerancy and Spontaneous Recall.- 5.2.3 Optimization and Search by Spatiotemporal Chaos as Spatiotemporally Structured Noise.- 5.2.4 Local-Global Transformation by Traveling Waves Information Creation and Transmission by Chaotic Traveling Waves.- 5.2.5 Selective Amplification of Input Signals by the Unidirectionally Coupled Map Lattice.- 5.3 Information Dynamics of a CML with One-Way Coupling.- 5.4 Design of Coupled Maps and Plastic Dynamics.- 5.5 Construction of Dynamic Many-to-Many Logic and Information Processing.- 5.6 Implications to Biological Networks.- 5.6.1 Prototype of Hierarchical Structures.- 5.6.2 Prototype of Diversity and Differentiation.- 5.6.3 Formation and Collapse of Relationships.- 5.6.4 Clustering in Hypercubic Coupled Maps
- Self-organizing Genetic Algorithms.- 5.6.5 Homeochaos.- 5.6.6 Summing Up.- 6. Chaotic Information Processing in the Brain.- 6.1 Hermeneutics of the Brain.- 6.2 A Brief Comment on Hermeneutics (the Inside and the Outside).- 6.3 A Method for Understanding th e Brain and Mind - Internal Description.- 6.4 Evidence of Chaos in Nervous Systems.- 6.5 The Origin of Neurochaos.- 6.6 The Implications of Stochastic Renewal of Maps.- 6.6.1 Chaotic Game.- 6.6.2 Skew-Product Transformations.- 6.7 A Model for Dynamic Memory.- 6.8 A Model for Dynamically Linking Memories.- 6.9 Significance of Neurochaos.- 6.10 Temporal Coding.- 6.11 Capillary Chaos as a Complex Dynamics.- 6.11.1 Significance of Capillary Pulsation in the Brain Functions.- 6.11.2 Embedding Theorems.- 6.11.3 Experimental Systems.- 6.11.4 Reconstruction of the Dynamics.- 6.11.5 Calculations of Lyapunov Exponents.- 6.11.6 The Condition Dependence.- 6.11.7 Cardiac Chaos.- 6.11.8 Information Structure.- 6.11.9 Implication s of Capillary Chaos.- 7. Conversations with Authors.- 7.1 Concluding Discussions.- 7.2 Questions and Answers.- 7.2.1 The Significance of Models in Complex Systems Research.- 7.2.2 Chaotic Itinerancy.- 7.2.3 New Information Theory and Internal Observation.- References.
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