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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.

Inhaltsverzeichnis

Frontmatter

1. Necessity for a Science of Complex Systems

Abstract
Why is a science of complex systems necessary?
Kunihiko Kaneko, Ichiro Tsuda

2. Observation Problems from an Information-Theoretical Viewpoint

Abstract
If chaos could be characterized by one word, it would be “complexity”. Even with the greatest of efforts, a finite sequence cannot accurately describe chaos. Chaos can be perfectly represented only in an infinite sequence. Several problems stemming from the discrepancy between this infiniteness and the finiteness of observation and description will be discussed later, but here we briefly touch upon it.
Kunihiko Kaneko, Ichiro Tsuda

3. CMLs: Constructive Approach to Spatiotemporal Chaos

Abstract
In physics, we are used to adopting a descriptive approach of nature. Often, one might assume that the macroscopic level of nature can be understood based on an understanding of the microscopic level. For example, the following chart flow is often applicable.
Kunihiko Kaneko, Ichiro Tsuda

4. Networks of Chaotic Elements

Abstract
As an example of the high-dimensional dynamics discussed in Chap. 1, let us consider a network of chaotic elements. In a network system many elements that can display chaotic dynamics interact with each other and evolve in time. Here we introduce the globally coupled map (GCM) as the simplest example of such a network of chaotic elements. We discuss the observed phenomena and th e universal concepts revealed therein in some detail, since the model provides us with a ‘dynamic many-to-many relationship’, ‘constructive model’, and ‘dynamics between the whole and its parts’. We believe that through the study of the GCM, we can work towards a methodology studying complex systems.
Kunihiko Kaneko, Ichiro Tsuda

5. Significance of Coupled Chaotic Systems to Biological Networks

Abstract
While in the next chapter neural information processing will be discussed from the viewpoint of chaos, here we briefly survey the significance of the CML and the GCM to biological information processing and to the complexity of living systems. We will also mention their applicability to engineering problems. Some of the conclusions of the current chapter will be important for the dynamic brain processes to be discussed in Chap.6 [Tsuda 1990a].
Kunihiko Kaneko, Ichiro Tsuda

6. Chaotic Information Processing in the Brain

Abstract
Let us call a machine involving simple stimulus-response rules a Cartesian automaton, and call a Cartesian automaton possessing a control system including feedback systems a Craik automaton [Johnson-Laird 1983]. By the studies of Karl von Frish, it turned out that a honey bee calculates the positions of flowers in relation to the position of the sun, and correctly sends such information to other bees. This seems to be a kind of sophisticated information processing, but its processing mechanism is essentially the same as that of a Craik automaton. The reason is as follows. Once the control system is set up, it performs correct calculations and outputs the results correctly, based on the present state and the purpose. In other words, the same result is output, provided the conditions are the same.
Kunihiko Kaneko, Ichiro Tsuda

7. Conversations with Authors

Abstract
In this final chapter we would like to review the current book by organizing the issues and novel viewpoints in aseries of question and answer sessions with the editors.
Kunihiko Kaneko, Ichiro Tsuda

Backmatter

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