Complex Systems: Chaos and Beyond: A Constructive Approach with Applications in Life Sciences

ISBN-13: 9783642631320 / Angielski / Miękka / 2012 / 274 str.

Kunihiko Kaneko; Ichiro Tsuda

Opis

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.

Recenzje

From the reviews:

SIAM REVIEW

"To sum up, the book should be a must-read for those interested in the modeling of coupled nonlinear systems...the interest of the global view of complexity that it provides makes it a highly recommendable read."

Spis treści

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.

Blurb

Chaos in science has always been a fascinating realm since it challenges the usual scientific approach of reductionism. While carefully distinguishing between complexity, holism, randomness, incompleteness, nondeterminism and stochastic behaviour the authors show that, although many aspects of chaos have been phenomenologically understood, most of its defining principles are still difficult to grasp and formulate. Demonstrating that chaos escapes all traditional methods of description, the authors set out to find new methods to deal with this phenomenon and illustrate their constructive approach with many examples from physics, biology and information technology. While maintaining a high level of rigour, an overly complicated mathematical apparatus is avoided in order to make this book accessible, beyond the specialist level, to a wider interdisciplinary readership.