Low-dimensional dynamics and bifurcations in oscillator networks via bi-orthogonal spectral decomposition
| Autor: | Jürgen Schwarz, K. Bräuer, Gerhard Dangelmayr, Andreas Stevens |
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| Rok vydání: | 2000 |
| Předmět: |
Van der Pol oscillator
Bistability General Physics and Astronomy Statistical and Nonlinear Physics Matrix decomposition Control theory Hierarchical control system Limit (mathematics) Statistical physics Mathematical Physics Energy (signal processing) Eigenvalues and eigenvectors Bifurcation Mathematics |
| Zdroj: | Journal of Physics A: Mathematical and General. 33:3555-3566 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/33/18/303 |
| Popis: | Many natural neural systems are functionally or hierarchically organized into interacting ensembles of neural populations. To investigate the dynamics in a hierarchical system of coupled bistable van der Pol oscillators we apply the bi-orthogonal decomposition into empirical orthogonal spatial and temporal modes. Within this method the dynamics and synchronized patterns are characterized by global, temporal and spatial entropy and energy. Different states of the network activity are identified as synchronous or asynchronous dynamics induced by external periodic input. Of particular interest is the ability of the bi-orthogonal decomposition to detect bifurcations following variations of the system parameter. Bifurcations correspond to crossings of the eigenvalues where an exchange of dominant modes takes place. In our simulations we observe a bifurcation induced by variations of input frequency and strength, identified as a saddle-node bifurcation of the unstable/stable pair of limit cycles. |
| Databáze: | OpenAIRE |
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