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Journal Article

Solvable Dynamics of Coupled High-Dimensional Generalized Limit-Cycle Oscillators


Zou,  Wei
External Organizations;

He,  Sujuan
External Organizations;

Senthilkumar,  D. V.
External Organizations;


Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Zou, W., He, S., Senthilkumar, D., Kurths, J. (2023): Solvable Dynamics of Coupled High-Dimensional Generalized Limit-Cycle Oscillators. - Physical Review Letters, 130, 10, 107202.

Cite as: https://publications.pik-potsdam.de/pubman/item/item_28463
We introduce a new model consisting of globally coupled high-dimensional generalized limit-cycle oscillators, which explicitly incorporates the role of amplitude dynamics of individual units in the collective dynamics. In the limit of weak coupling, our model reduces to the D-dimensional Kuramoto phase model, akin to a similar classic construction of the well-known Kuramoto phase model from weakly coupled two-dimensional limit-cycle oscillators. For the practically important case of D=3, the incoherence of the model is rigorously proved to be stable for negative coupling (K<0) but unstable for positive coupling (K>0); the locked states are shown to exist if K>0; in particular, the onset of amplitude death is theoretically predicted. For D≥2, the discrete and continuous spectra for both locked states and amplitude death are governed by two general formulas. Our proposed D-dimensional model is physically more reasonable, because it is no longer constrained by fixed amplitude dynamics, which puts the recent studies of the D-dimensional Kuramoto phase model on a stronger footing by providing a more general framework for D-dimensional limit-cycle oscillators.