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The Lohe tensor model is a first-order tensor-valued continuous-time modelfor the aggregation of tensors with the same rank and size. It reduces towell-known aggregation models such as the Kuramoto model, the Lohe sphere modeland the Lohe matrix model as special cases for low-rank tensors. We present asufficient and necessary framework for the solution splitting property(SSP) andanalyze two possible asymptotic states(completely aggregate state and bi-polarstate) which can emerge from a set of initial data. Moreover, we provide asufficient framework leading to the aforementioned two asymptotic states interms of initial data and system parameters.

Complete aggregation of the Lohe tensor model with the same free flow