By K. Kudo, E.R. Nakamura, O. Yamakawa, Y. Tamagawa

Nonlinear complicated open platforms express nice variety within the technique of self-organization, and that variety raises as complexity raises. The dimension of complexity and the origins of the range of such advanced structures are the focal point of interdisciplinary stories extending throughout a variety of medical disciplines that come with utilized arithmetic, physics, chemistry, biology, psychology, ecology, sociology, and economics. earlier investigations have centred both on complexity or on range, yet now not either. This quantity makes transparent the relation among complexity and variety with examples drawn from a number of disciplines. Compiles listed below are shows from the Complexity and variety workshop held in Fugue, Japan, in August 1996. The contributions are the result of study in mathematical structures, actual platforms, dwelling structures, and social platforms, and are inside the 4 corresponding sections of the ebook. Mathematical expressions for the speculation of complexity as a basic strategy in addition to real looking examples for program of systematic tools give you the reader with prepared entry to the most recent issues in advanced systems.

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**Example text**

Zfalsc(:r) = Ztnte(1- x). Then. we obtained the functional equations. T n+l' Y,,+I) gn+l(:7:,,+I, Y"+l) 1, g,,(:r n , y,,). r and y. e .. 13-16. The function g is a similar one for the truth value y. 1" and y, respecti\"ely. \Ve call the dynamics of l' and y a lower dynamics, and the dynamics of f and g a higher dynamics. Here a lower and a higher dynamics are almost identical, only the difference of which comes from the relation 21. By a usage of se\"eral techniques, one can solve these functional equations.

The temporal pattern of the clustering is robust against external noise or is deterministic even if differences in the initial state are given stochastically. Our model takes into account of the feature of the globally coupled chaotic system, while the change in the degree of freedom is brought about by the cell division in the course of cell differentiation, which is also noted as a novel dynamical systems problem termed open chaos [8, 9]. Although we hope to reinterpret the cell biology [12] from our inter-intra dynamics viewpoint, it may be interesting, for the moment, to point out two experimental results.

The growth of iriformational and computational ecosystems is connected with a fundamental change of society characterized by a switch from traditional industries handling goods to knowledge industries for information and an economy of information services. The production, distribution, and administration of information have become the main acitivites of modem knowledge based societies. Thus, the interface between humans and information systems must be continously improved in order to realize the ideal of worldwide human communication.