Collective dynamics in two populations of noisy oscillators with asymmetric interactions
We study two intertwined globally coupled networks of noisy Kuramoto phase oscillators that have the same natural frequency, but differ in their perception of the mean field and their contribution to it. Such a give-and-take mechanism is given by asymmetric in- and out-coupling strengths which can b...
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| Veröffentlicht in: | arXiv.org 2015-06 |
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| creator | Sonnenschein, Bernard DM Peron, Thomas K Rodrigues, Francisco A Kurths, Jürgen Schimansky-Geier, Lutz |
| description | We study two intertwined globally coupled networks of noisy Kuramoto phase oscillators that have the same natural frequency, but differ in their perception of the mean field and their contribution to it. Such a give-and-take mechanism is given by asymmetric in- and out-coupling strengths which can be both positive and negative. We uncover in this minimal network of networks intriguing patterns of discordance, where the ensemble splits into two clusters separated by a constant phase lag. If it differs from \(\pi\), then traveling wave solutions emerge. We observe a second route to traveling waves via traditional one-cluster states. Bistability is found between the various collective states. Analytical results and bifurcation diagrams are derived with a reduced system. |
| doi_str_mv | 10.48550/arxiv.1503.04922 |
| format | Article |
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Such a give-and-take mechanism is given by asymmetric in- and out-coupling strengths which can be both positive and negative. We uncover in this minimal network of networks intriguing patterns of discordance, where the ensemble splits into two clusters separated by a constant phase lag. If it differs from \(\pi\), then traveling wave solutions emerge. We observe a second route to traveling waves via traditional one-cluster states. Bistability is found between the various collective states. 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| subjects | Bifurcations Bistability Oscillators Phase lag Physics - Adaptation and Self-Organizing Systems Physics - Disordered Systems and Neural Networks Physics - Statistical Mechanics Resonant frequencies Traveling waves |
| title | Collective dynamics in two populations of noisy oscillators with asymmetric interactions |
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