文档介绍：Discrete Dynamics in Nature and Society, Vol. 1, pp. 1-8 (C) 1997 OPA (Overseas Publishers Association)
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Discrete Dynamics plex Systems
HERMANN HAKEN
Institute for Theoretical Physics and Synergetics, University of Stuttgart, Pfaffenwaldring 57/4, D-70550 Stuttgart, Germany
(Received 9 October 1996)
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 multiplica-
tive 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 equa-
tions 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.
Keywords." Discrete dynamics, Difference equations, Noise, Synergetics, Slaving principle,
Complex systems
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