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Entropy 2016, 18(3), 74; doi:10.3390/e18030074

Self-Organization with Constraints—A Mathematical Model for Functional Differentiation

1
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan
2
Department of Computer Science and Engineering, Fukuoka Institute of Technology, Fukuoka 811-0214, Japan
*
Author to whom correspondence should be addressed.
Academic Editors: Hermann Haken and Juval Portugali
Received: 21 October 2015 / Revised: 10 February 2016 / Accepted: 22 February 2016 / Published: 26 February 2016
(This article belongs to the Special Issue Information and Self-Organization)
View Full-Text   |   Download PDF [1271 KB, uploaded 26 February 2016]   |  

Abstract

This study proposes mathematical models for functional differentiations that are viewed as self-organization with external constraints. From the viewpoint of system development, the present study investigates how system components emerge under the presence of constraints that act on a whole system. Cell differentiation in embryos and functional differentiation in cortical modules are typical examples of this phenomenon. In this paper, as case studies, we deal with three mathematical models that yielded components via such global constraints: the genesis of neuronal elements, the genesis of functional modules, and the genesis of neuronal interactions. The overall development of a system may follow a certain variational principle. View Full-Text
Keywords: self-organization; functional differentiation; chaotic itinerancy; variational principle; neuron; cortical organization self-organization; functional differentiation; chaotic itinerancy; variational principle; neuron; cortical organization
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Tsuda, I.; Yamaguti, Y.; Watanabe, H. Self-Organization with Constraints—A Mathematical Model for Functional Differentiation. Entropy 2016, 18, 74.

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