Abstract: Synchronization in Kuramoto-type oscillator systems is commonly described using several notions, including phase locking, frequency synchronization, and order-parameter coherence. In this talk we present a dynamical perspective explaining why these notions are equivalent for real Kuramoto flows. For first-order, second-order, and hybrid models with heterogeneous parameters and coupling structures, we show that synchronization corresponds to an equilibrium phenomenon: after reduction to a co-rotating frame, the long-time dynamics collapse to equilibrium states. Motivated by this viewpoint, we then consider the complexified Kuramoto model. In contrast to the real case, the complexified system admits new dynamical phenomena such as periodic orbits, homoclinic structures, and finite-time blow-up. These recurrent dynamics break the equivalence of synchronization notions and lead to qualitatively different collective behavior.

 

Link Information:  WEBEX MEETING https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m6563fb0c7e9d795078f1b8e0001ec93f

Meeting number (access code): 2511 971 9604

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Organizer: Chueh-Hsin Chang (CCU), Jia-Yuan Dai (NTHU), Bo-Chih Huang (CCU), Chih-Chiang Huang (CCU), Chang-Hong Wu (NYCU)