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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1026022697000022 |
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| 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. |
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| ISSN: | 1026-0226 1607-887X |