Complex Systems: Chaos and Beyond

A Constructive Approach with Applications in Life Sciences

By: Kunihiko Kaneko, Ichiro Tsuda

Write A Review

Hardcover | 4 October 2000

At a Glance

Hardcover
292 Pages

Dimensions(cm)
23.5 x 15.88 x 1.91

Hardcover

$169.00

or 4 interest-free payments of $42.25 with

Ships in 5 to 7 business days

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.

Industry Reviews

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."

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Chaos Theory Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory Science Astronomy, Space & Time Nonlinear Science Physics

Mathematical Physics

Necessity for a Science of Complex Systems	p. 1
Introduction	p. 1
Chaos	p. 4
Chaos and Complexity	p. 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 Errors	p. 11
Dialectic Method to Overcome the Antithesis Between Order and Randomness	p. 12
Beyond the Antithesis Between Reductionism and Holism	p. 12
Dynamic Many-to-Many Relations and Bio-networks	p. 13
The Necessity of Dynamic Many-to-Many Relations	p. 13
Metabolic Systems, Differentiation, and Development	p. 15
Ecosystems	p. 16
Immune Systems	p. 17
The Brain	p. 18
Rugged Landscapes and Their Problems	p. 18
Conclusion	p. 20
The Construction of an Artificial (Virtual) World	p. 21
A Trigger to Emergence	p. 24
Beyond Top-Down Versus Bottom-Up	p. 26
Methodology of Study of Complex Systems	p. 28
Constructive Way of Understanding	p. 29
Plural Views	p. 30
Mathematical Anatomy	p. 31
The Problem ofInternal Observers	p. 31
Observation Problems from an Information-Theoretical Viewpoint	p. 33
Observation Problems ofChaos	p. 33
Undecidability and Entire Description	p. 37
A Demon in Chaos	p. 38
Chaos in the BZ Reaction	p. 39
Noise-Induced Order	p. 43
Could Structural Stability Lead to an Adequate Notion of a Model?	p. 47
Information Theory of Chaos	p. 50
CMLs: Constructive Approach to Spatiotemporal Chaos	p. 57
From a Descriptive to a Constructive Approach of Nature	p. 57
Coupled Map Lattice Approach to Spatiotemporal Chaos	p. 59
Spatiotemporal Chaos	p. 59
Introduction to Coupled Map Lattices	p. 61
Comparison with Other Approaches	p. 64
Phenomenology of Spatiotemporal Chaos in the Diffusively Coupled Logistic Lattice	p. 65
Introduction	p. 65
Frozen Random Patterns and Spatial Bifurcations	p. 66
Pattern Selection with Suppression of Chaos	p. 69
Brownian Motion of Chaotic Defects and Defect Turbulence	p. 70
Spatiotemporal Intermittency (STI)	p. 71
Stability of Fully Developed Spatiotemporal Chaos (FDSTC) Sustained by the Supertransients	p. 75
Traveling Waves	p. 77
Supertransients	p. 81
CML Phenomenology as a Problem of Complex Systems	p. 83
Phenonemology in Open-Flow Lattices	p. 84
Introduction	p. 84
Spatial Bifurcation to Down-Flow	p. 85
Convective Instability and Spatial Amplification of Fluctuations	p. 86
Phase Diagram	p. 89
Spatial Chaos	p. 91
Selective Amplification of Input	p. 93
Universality	p. 94
Theory for Spatiotemporal Chaos	p. 97
Applications of Coupled Map Lattices	p. 100
Pattern Formation (Spinodal Decomposition)	p. 100
Crystal Growth and Boiling	p. 101
Convection	p. 101
Spiral and Traveling Waves in Excitable Media	p. 103
Cloud Dynamics and Geophysics	p. 104
Ecological Systems	p. 104
Evolution	p. 104
Closing Remarks	p. 105
Networks of Chaotic Elements	p. 107
GCM Model	p. 107
Clustering	p. 111
Phase Transitions Between Clustering States	p. 115
Ordered Phase and Cluster Bifurcation	p. 117
Hierarchical Clustering and Chaotic Itinerancy	p. 122
Partition Complexity	p. 122
Hierarchical Clustering	p. 125
Hierarchical Dynamics	p. 128
Chaotic Itinerancy	p. 132
Marginal Stability and Information Cascade	p. 135
Marginal Stability	p. 135
Information Cascade	p. 139
Collective Dynamics	p. 143
Remnant Mean-Field Fluctuation	p. 143
Hidden Coherence	p. 146
Instability of the Fixed Point of the Perron-Frobenius Operator	p. 150
Destruction of Hidden Coherence by Noise and Anomalous Fluctuations	p. 153
Heterogeneous Systems	p. 155
Significance of Collective Dynamics	p. 156
Universality and Nonuniversality	p. 157
Universality of Clustering and Other Transitions	p. 157
Globally Coupled Tent Map: Novelty Within Universality	p. 159
Significance of Coupled Chaotic Systems to Biological Networks	p. 163
Relevance of Coupled Maps to Biological Information Processing	p. 163
Application of Coupled Maps to Information Processing	p. 164
Memory to Attractor Mapping and the Switching Process	p. 164
Chaotic Itinerancy and Spontaneous Recall	p. 168
Optimization and Search by Spatiotemporal Chaos as Spatiotemporally Structured Noise	p. 170
Local-Global Transformation by Traveling Waves - Information Creation and Transmission by Chaotic Traveling Waves	p. 170
Selective Amplification of Input Signals by the Unidirectionally Coupled Map Lattice	p. 170
Information Dynamics of a CML with One-Way Coupling	p. 171
Design of Coupled Maps and Plastic Dynamics	p. 175
Construction of Dynamic Many-to-Many Logic and Information Processing	p. 178
Implications to Biological Networks	p. 179
Prototype of Hierarchical Structures	p. 180
Prototype of Diversity and Differentiation	p. 180
Formation and Collapse of Relationships	p. 184
Clustering in Hypercubic Coupled Maps;Self-organizing Genetic Algorithms	p. 184
Homeochaos	p. 186
Summing Up	p. 189
Chaotic Information Processing in the Brain	p. 191
Hermeneutics of the Brain	p. 191
A Brief Comment on Hermeneutics (the Inside and the Outside)	p. 194
A Method for Understanding the Brain and Mind - Internal Description	p. 195
Evidence of Chaos in Nervous Systems	p. 196
The Origin of Neurochaos	p. 198
The Implications of Stochastic Renewal of Maps	p. 203
Chaotic Game	p. 203
Skew-Product Transformations	p. 204
A Model for Dynamic Memory	p. 205
A Model for Dynamically Linking Memories	p. 206
Significance of Neurochaos	p. 212
Temporal Coding	p. 214
Capillary Chaos as a Complex Dynamics	p. 219
Significance of Capillary Pulsation in the Brain Functions	p. 219
Embedding Theorems	p. 220
Experimental Systems	p. 221
Reconstruction of the Dynamics	p. 222
Calculations of Lyapunov Exponents	p. 224
The Condition Dependence	p. 226
Cardiac Chaos	p. 230
Information Structure	p. 231
Implications of Capillary Chaos	p. 235
Conversations with Authors	p. 237
Concluding Discussions	p. 237
Questions and Answers	p. 239
The Significance of Models in Complex Systems Research	p. 239
Chaotic Itinerancy	p. 243
New Information Theory and Internal Observation	p. 246
References	p. 251
Index	p. 267
Table of Contents provided by Publisher. All Rights Reserved.

Complex Systems: Chaos and Beyond

A Constructive Approach with Applications in Life Sciences

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Mathematical Physics

Undergraduate Lecture Notes in Physics

A Practical Guide with Problems and Solutions

Lectures on Theoretical Optics

Graduate Texts in Physics

Quantum Physics For Dummies

For Dummies

General Relativity

The Theoretical Minimum

Inverse Problems

in Memory of Professor Zbigniew Oziewicz

Noncommutative measures and Orlicz Spaces, with Applications to Quantum Physic

Oxford Graduate Texts in Mathematics

Statistical Physics

An Introductory Course

Scattering of Waves

Theory and Applications

Fluid Universe

The Way of Structured Water and its Mathematical Foundations

Elements of Topology

Theory and Practice

Computational Physics Using Python

Computational Physics Using Python

Abstract Cauchy Problems

Three Approaches

Is Mind Just a Computation?

How Computer Science Dispels the Myths of the Age of AI

Darboux Transformation of Nonlinear Schr¶dinger Equations

A Guide and a Tutorial

Mathematical Advances in Theoretical Chemistry

Developments in Physical & Theoretical Chemistry

Gauge Fields, Knots And Gravity

Series on Knots & Everything

Mathematical Methods for Physics and Engineering

Practical Applications

Mathematical Methods for Physics and Engineering

Practical Applications

Dynamics and Astrophysics of Galaxies

Princeton Series in Astrophysics

Dynamics and Astrophysics of Galaxies

Princeton Series in Astrophysics

Categorical and Enumerative Aspects of Mirror Symmetry

A Tribute to the Life and Work of Professor Bumsig Kim

Proper Time and Mass as Dynamical Variables

Why it's Possible and Some Consequences

Schur Analysis and Applications to Hypercomplex Analysis, Neural Networks, and Linear Systems

Chapman University, January 2024

This product is categorised by