Next Article in Journal
Off-Design Modeling of Natural Gas Combined Cycle Power Plants: An Order Reduction by Means of Thermoeconomic Input–Output Analysis
Next Article in Special Issue
An Evolutionary Game Theoretic Approach to Multi-Sector Coordination and Self-Organization
Previous Article in Journal / Special Issue
Measuring the Complexity of Continuous Distributions
Article Menu

Export Article

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

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

Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan
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]   |  


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

Figure 1

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).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top