Emergent behaviors of Lohe tensor flocks

Seung-Yeal Ha, Seoul National University
4/28, 2021 at 4:10PM-5PM in https://berkeley.zoom.us/j/186935273

In this talk, we present a new aggregation model on the space of rank-m tensors with the same size, and study emergent dynamics of the proposed model. Our proposed aggregation model is general enough to include Lohe type synchronization models such as the Kuramoto model, the Lohe sphere model and the Lohe matrix models for the ensemble of real rank-0, rank-1 and rank-2 tensors, respectively. In this regard, we call our proposed model as the Lohe tensor model for rank-m tensors with the same size. For the proposed model, we present several sufficient frameworks leading to the collective dynamics of the Lohe tensor model in terms of system parameters and initial data, and study existence of special solutions such as completely separable solutions and quadratically separable solutions. This is a joint work with Hansol Park (Seoul National Univ.) and Dohyun Kim (Sungshin Women’s Univ.)