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

Speaker: Prof. Wei Zou (South China Normal University, China)

Time: April 25, 15:00

Venue: Lecture Hall, Room 213, 2nd Floor, Physical Building (Building 18), Guangzhou Wushan Campus

[Abstract]

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.

Announced by School of Physics and Optoelectronics