The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization, and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The Sakaguchi-Kuramoto model is a generalization of the basic model that considers the presence of a phase-lag parameter in the interaction, thereby making it asymmetric between oscillator pairs. Here, we consider a further generalization, by adding an interaction that breaks the rotational symmetry of the model. The highlight of our study is the unveiling of a very rich phase diagram comprising both oscillatory and non-oscillatory synchronized phases as well as an incoherent phase: There are regions of two-phase as well as an interesting and hitherto unexplored three-phase coexistence arising from asymmetric interactions in our model.
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Posted 19 Mar, 2021
Received 16 Mar, 2021
On 04 Mar, 2021
On 01 Mar, 2021
Posted 19 Mar, 2021
Received 16 Mar, 2021
On 04 Mar, 2021
On 01 Mar, 2021
The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization, and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The Sakaguchi-Kuramoto model is a generalization of the basic model that considers the presence of a phase-lag parameter in the interaction, thereby making it asymmetric between oscillator pairs. Here, we consider a further generalization, by adding an interaction that breaks the rotational symmetry of the model. The highlight of our study is the unveiling of a very rich phase diagram comprising both oscillatory and non-oscillatory synchronized phases as well as an incoherent phase: There are regions of two-phase as well as an interesting and hitherto unexplored three-phase coexistence arising from asymmetric interactions in our model.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
This preprint is available for download as a PDF.
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