Discrete dynamics of complex systems

This article extends the slaving principle of synergetics to processes with discrete time steps. Starting point is a set of nonlinear difference equations which contain multiplicative noise and which refer to multidimensional state vectors. The system depends on a control parameter. When its value i...

Full description

Saved in:
Bibliographic Details
Main Author: Hermann Haken
Format: Article
Language:English
Published: Wiley 1997-01-01
Series:Discrete Dynamics in Nature and Society
Subjects:
Online Access:http://dx.doi.org/10.1155/S1026022697000022
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article extends the slaving principle of synergetics to processes with discrete time steps. Starting point is a set of nonlinear difference equations which contain multiplicative noise and which refer to multidimensional state vectors. The system depends on a control parameter. When its value is changed beyond a critical value, an instability of the solution occurs. The stability analysis allows us to divide the system into stable and unstable modes. The original equations can be transformed to a set of difference equations for the unstable and stable modes. The extension of the slaving principle to the time-discrete case then states that all the stable modes can be explicitly expressed by the unstable modes or so-called order-parameters.
ISSN:1026-0226
1607-887X