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

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Springer Science & Business Media, 2001 - Mathematics - 273 pages
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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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Contents

1 Necessity for a Science of Complex Systems
1
12 Chaos
4
13 Chaos and Complexity
8
14 How Has Chaos Changed Our Way of Thinking?
11
142 Dialectic Method to Overcome the Antithesis Between Order and Randomness
12
15 Dynamic ManytoMany Relations and Bionetworks
13
152 Metabolic Systems Differentiation and Development
15
153 Ecosystems
16
44 Ordered Phase and Cluster Bifurcation
117
45 Hierarchical Clustering and Chaotic Itinerancy
122
452 Hierarchical Clustering
125
453 Hierarchical Dynamics
128
454 Chaotic Itinerancy
132
46 Marginal Stability and Information Cascade
135
462 Information Cascade
139
47 Collective Dynamics
143

154 Immune Systems
17
155 The Brain
18
157 Conclusion
20
16 The Construction of an Artificial Virtual World
21
17 A Trigger to Emergence
24
18 Beyond TopDown Versus BottomUp
26
19 Methodology of Study of Complex Systems
28
191 Constructive Way of Understanding
29
192 Plural Views
30
193 Mathematical Anatomy
31
2 Observation Problems from an InformationTheoretical Viewpoint
33
22 Undecidability and Entire Description
37
23 A Demon in Chaos
38
24 Chaos in the BZ Reaction
39
25 NoiseInduced Order
43
26 Could Structural Stability Lead to an Adequate Notion of a Model?
47
27 Information Theory of Chaos
50
Constructive Approach to Spatiotemporal Chaos
57
32 Coupled Map Lattice Approach to Spatiotemporal Chaos
59
322 Introduction to Coupled Map Lattices
61
323 Comparison with Other Approaches
64
33 Phenomenology of Spatiotemporal Chaos in the Diffusively Coupled Logistic Lattice
65
332 Frozen Random Patterns and Spatial Bifurcations
66
333 Pattern Selection with Suppression of Chaos
69
334 Brownian Motion of Chaotic Defects and Defect Turbulence
70
335 Spatiotemporal Intermittency STI
71
336 Stability of Fully Developed Spatiotemporal Chaos FDSTC Sustained by the Supertransients
75
337 Traveling Waves
77
338 Supertransients
81
34 CML Phenomenology as a Problem of Complex Systems
83
35 Phenonemology in OpenFlow Lattices
84
352 Spatial Bifurcation to DownFlow
85
353 Convective Instability and Spatial Amplification of Fluctuations
86
354 Phase Diagram
89
355 Spatial Chaos
91
356 Selective Amplification of Input
93
36 Universality
94
37 Theory for Spatiotemporal Chaos
97
38 Applications of Coupled Map Lattices
100
382 Crystal Growth and Boiling
101
384 Spiral and Traveling Waves in Excitable Media
103
385 Cloud Dynamics and Geophysics
104
388 Closing Remarks
105
4 Networks of Chaotic Elements
107
42 Clustering
111
43 Phase Transitions Between Clustering States
115
472 Hidden Coherence
146
473 Instability of the Fixed Point of the PerronFrobenius Operator
150
474 Destruction of Hidden Coherence by Noise and Anomalous Fluctuations
153
475 Heterogeneous Systems
155
476 Significance of Collective Dynamics
156
48 Universality and Nonuniversality
157
Novelty Within Universality
159
5 Significance of Coupled Chaotic Systems to Biological Networks
163
52 Application of Coupled Maps to Information Processing
164
522 Chaotic Itinerancy and Spontaneous Recall
168
523 Optimization and Search by Spatiotemporal Chaos as Spatiotemporally Structured Noise
170
53 Information Dynamics of a CML with OneWay Coupling
171
54 Design of Coupled Maps and Plastic Dynamics
175
55 Construction of Dynamic ManytoMany Logic and Information Processing
178
56 Implications to Biological Networks
179
561 Prototype of Hierarchical Structures
180
563 Formation and Collapse of Relationships
184
565 Homeochaos
186
566 Summing Up
189
6 Chaotic Information Processing in the Brain
191
62 A Brief Comment on Hermeneutics the Inside and the Outside
194
63 A Method for Understanding the Brain and Mind Internal Description
195
64 Evidence of Chaos in Nervous Systems
196
65 The Origin of Neurochaos
198
66 The Implications of Stochastic Renewal of Maps
203
662 SkewProduct Transformations
204
67 A Model for Dynamic Memory
205
68 A Model for Dynamically Linking Memories
206
69 Significance of Neurochaos
212
610 Temporal Coding
214
611 Capillary Chaos as a Complex Dynamics
219
6112 Embedding Theorems
220
6113 Experimental Systems
221
6114 Reconstruction of the Dynamics
222
6115 Calculations of Lyapunov Exponents
224
6116 The Condition Dependence
226
6117 Cardiac Chaos
230
6118 Information Structure
231
6119 Implications of Capillary Chaos
235
7 Conversations with Authors
237
72 Questions and Answers
239
722 Chaotic Itinerancy
243
723 New Information Theory and Internal Observation
246
References
251
Index
267
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