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

Complex Systems: Chaos and Beyond

A Constructive Approach with Applications in Life Sciences

Hardcover Published: 4th October 2000
ISBN: 9783540672029
Number Of Pages: 274

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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.

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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."

Necessity for a Science of Complex Systemsp. 1
Introductionp. 1
Chaosp. 4
Chaos and Complexityp. 8
How Has Chaos Changed Our Way of Thinking?p. 11
Dialectic Method to Overcome the Antithesis Between Determinism and Nondeterminism or Between Programs and Errorsp. 11
Dialectic Method to Overcome the Antithesis Between Order and Randomnessp. 12
Beyond the Antithesis Between Reductionism and Holismp. 12
Dynamic Many-to-Many Relations and Bio-networksp. 13
The Necessity of Dynamic Many-to-Many Relationsp. 13
Metabolic Systems, Differentiation, and Developmentp. 15
Ecosystemsp. 16
Immune Systemsp. 17
The Brainp. 18
Rugged Landscapes and Their Problemsp. 18
Conclusionp. 20
The Construction of an Artificial (Virtual) Worldp. 21
A Trigger to Emergencep. 24
Beyond Top-Down Versus Bottom-Upp. 26
Methodology of Study of Complex Systemsp. 28
Constructive Way of Understandingp. 29
Plural Viewsp. 30
Mathematical Anatomyp. 31
The Problem ofInternal Observersp. 31
Observation Problems from an Information-Theoretical Viewpointp. 33
Observation Problems ofChaosp. 33
Undecidability and Entire Descriptionp. 37
A Demon in Chaosp. 38
Chaos in the BZ Reactionp. 39
Noise-Induced Orderp. 43
Could Structural Stability Lead to an Adequate Notion of a Model?p. 47
Information Theory of Chaosp. 50
CMLs: Constructive Approach to Spatiotemporal Chaosp. 57
From a Descriptive to a Constructive Approach of Naturep. 57
Coupled Map Lattice Approach to Spatiotemporal Chaosp. 59
Spatiotemporal Chaosp. 59
Introduction to Coupled Map Latticesp. 61
Comparison with Other Approachesp. 64
Phenomenology of Spatiotemporal Chaos in the Diffusively Coupled Logistic Latticep. 65
Introductionp. 65
Frozen Random Patterns and Spatial Bifurcationsp. 66
Pattern Selection with Suppression of Chaosp. 69
Brownian Motion of Chaotic Defects and Defect Turbulencep. 70
Spatiotemporal Intermittency (STI)p. 71
Stability of Fully Developed Spatiotemporal Chaos (FDSTC) Sustained by the Supertransientsp. 75
Traveling Wavesp. 77
Supertransientsp. 81
CML Phenomenology as a Problem of Complex Systemsp. 83
Phenonemology in Open-Flow Latticesp. 84
Introductionp. 84
Spatial Bifurcation to Down-Flowp. 85
Convective Instability and Spatial Amplification of Fluctuationsp. 86
Phase Diagramp. 89
Spatial Chaosp. 91
Selective Amplification of Inputp. 93
Universalityp. 94
Theory for Spatiotemporal Chaosp. 97
Applications of Coupled Map Latticesp. 100
Pattern Formation (Spinodal Decomposition)p. 100
Crystal Growth and Boilingp. 101
Convectionp. 101
Spiral and Traveling Waves in Excitable Mediap. 103
Cloud Dynamics and Geophysicsp. 104
Ecological Systemsp. 104
Evolutionp. 104
Closing Remarksp. 105
Networks of Chaotic Elementsp. 107
GCM Modelp. 107
Clusteringp. 111
Phase Transitions Between Clustering Statesp. 115
Ordered Phase and Cluster Bifurcationp. 117
Hierarchical Clustering and Chaotic Itinerancyp. 122
Partition Complexityp. 122
Hierarchical Clusteringp. 125
Hierarchical Dynamicsp. 128
Chaotic Itinerancyp. 132
Marginal Stability and Information Cascadep. 135
Marginal Stabilityp. 135
Information Cascadep. 139
Collective Dynamicsp. 143
Remnant Mean-Field Fluctuationp. 143
Hidden Coherencep. 146
Instability of the Fixed Point of the Perron-Frobenius Operatorp. 150
Destruction of Hidden Coherence by Noise and Anomalous Fluctuationsp. 153
Heterogeneous Systemsp. 155
Significance of Collective Dynamicsp. 156
Universality and Nonuniversalityp. 157
Universality of Clustering and Other Transitionsp. 157
Globally Coupled Tent Map: Novelty Within Universalityp. 159
Significance of Coupled Chaotic Systems to Biological Networksp. 163
Relevance of Coupled Maps to Biological Information Processingp. 163
Application of Coupled Maps to Information Processingp. 164
Memory to Attractor Mapping and the Switching Processp. 164
Chaotic Itinerancy and Spontaneous Recallp. 168
Optimization and Search by Spatiotemporal Chaos as Spatiotemporally Structured Noisep. 170
Local-Global Transformation by Traveling Waves - Information Creation and Transmission by Chaotic Traveling Wavesp. 170
Selective Amplification of Input Signals by the Unidirectionally Coupled Map Latticep. 170
Information Dynamics of a CML with One-Way Couplingp. 171
Design of Coupled Maps and Plastic Dynamicsp. 175
Construction of Dynamic Many-to-Many Logic and Information Processingp. 178
Implications to Biological Networksp. 179
Prototype of Hierarchical Structuresp. 180
Prototype of Diversity and Differentiationp. 180
Formation and Collapse of Relationshipsp. 184
Clustering in Hypercubic Coupled Maps;Self-organizing Genetic Algorithmsp. 184
Homeochaosp. 186
Summing Upp. 189
Chaotic Information Processing in the Brainp. 191
Hermeneutics of the Brainp. 191
A Brief Comment on Hermeneutics (the Inside and the Outside)p. 194
A Method for Understanding the Brain and Mind - Internal Descriptionp. 195
Evidence of Chaos in Nervous Systemsp. 196
The Origin of Neurochaosp. 198
The Implications of Stochastic Renewal of Mapsp. 203
Chaotic Gamep. 203
Skew-Product Transformationsp. 204
A Model for Dynamic Memoryp. 205
A Model for Dynamically Linking Memoriesp. 206
Significance of Neurochaosp. 212
Temporal Codingp. 214
Capillary Chaos as a Complex Dynamicsp. 219
Significance of Capillary Pulsation in the Brain Functionsp. 219
Embedding Theoremsp. 220
Experimental Systemsp. 221
Reconstruction of the Dynamicsp. 222
Calculations of Lyapunov Exponentsp. 224
The Condition Dependencep. 226
Cardiac Chaosp. 230
Information Structurep. 231
Implications of Capillary Chaosp. 235
Conversations with Authorsp. 237
Concluding Discussionsp. 237
Questions and Answersp. 239
The Significance of Models in Complex Systems Researchp. 239
Chaotic Itinerancyp. 243
New Information Theory and Internal Observationp. 246
Referencesp. 251
Indexp. 267
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540672029
ISBN-10: 3540672028
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 274
Published: 4th October 2000
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.75
Weight (kg): 0.59

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