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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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | Discrete Dynamics in Nature and Society |
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| Online Access: | http://dx.doi.org/10.1155/S1026022697000022 |
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| _version_ | 1849694509573603328 |
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| author | Hermann Haken |
| author_facet | Hermann Haken |
| author_sort | Hermann Haken |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fa3fd01e7a194a83b594d5cd34af075b |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-fa3fd01e7a194a83b594d5cd34af075b2025-08-20T03:20:03ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X1997-01-01111810.1155/S1026022697000022Discrete dynamics of complex systemsHermann Haken0Institute for Theoretical Physics and Synergetics, University of Stuttgart, Pfaffenwaldring 57/4, Stuttgart D-70550, GermanyThis 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.http://dx.doi.org/10.1155/S1026022697000022Discrete dynamicsDifference equationsNoiseSynergeticsSlaving principleComplex systems. |
| spellingShingle | Hermann Haken Discrete dynamics of complex systems Discrete Dynamics in Nature and Society Discrete dynamics Difference equations Noise Synergetics Slaving principle Complex systems. |
| title | Discrete dynamics of complex systems |
| title_full | Discrete dynamics of complex systems |
| title_fullStr | Discrete dynamics of complex systems |
| title_full_unstemmed | Discrete dynamics of complex systems |
| title_short | Discrete dynamics of complex systems |
| title_sort | discrete dynamics of complex systems |
| topic | Discrete dynamics Difference equations Noise Synergetics Slaving principle Complex systems. |
| url | http://dx.doi.org/10.1155/S1026022697000022 |
| work_keys_str_mv | AT hermannhaken discretedynamicsofcomplexsystems |