Finiteness of collisions and phase-locking for the Kuramoto model

Seung Yeal Ha

Seoul National University

  Abstract:We discuss relations between the finiteness of collisions and phase-locking of the Kuramoto model. When there is no inertial effect, it is well known that the finiteness of collisions is equivalent to the emergence of phase-locking. Thus, when a Kuramoto ensemble is under the effect of inertia, whether the same equivalence relation hold or not is an intricate question. In this talk, we show that in a small inertia regime, the aforementioned equivalence still holds, whereas in a large inertia regime, we show that a homogeneous Kuramoto ensemble with the same natural frequencies can exhibit phase-locking, while there are countable number of collisions between Kuramoto oscillators. This is a contrasted effect of a large inertia in phase-locking process. This talk is a based on the joint work with Hangjun Cho (SNU) and Jiu-Gang Dong (Dalian Univ. of Technology) in SIAM Journal on Applied Dynamical Systems.

The delayed Hegselmann-Krause opinion formation model under leader’s control

Du Linglong (杜玲珑)

Donghua University

    Abstract:We consider the Hegselmann-Krause opinion formation model with leadership and time delay. Numerical simulations suggest that the consensus can still emerge asymptotically in the opinion evolution flow under the leader's control even when the time delay is large. In this talk, we use an iterated framework to prove the consensus control behavior for the delayed Hegselmann-Krause model with leadership, without any restriction on the length of the time delay.  After that, we present a simple control strategy which can steer all agents to any target opinion. Numerical simulations are performed to confirm theoretical results. This is a joint work with Zhu jianwen and Xie feng.

  时间：2023年8月10日  9:00

  地点：理学楼609