Abstract
We present a first-order aggregation model on space of complex matrices which can be derived from Lohe tensor model on space of tensors with same rank and size. We call such matrix-valued aggregation model as the generalized Lohe matrix model. For proposed matrix model with two cubic coupling terms, we study several structural properties such as conservation laws, solution splitting property. In particular, for case of only one coupling, we reformulate reduced Lohe matrix model into Lohe matrix model with a diagonal frustration, and provide several sufficient frameworks leading to complete and practical aggregations. For estimates of collective dynamics, we use a nonlinear functional approach using an ensemble diameter which measures degree of aggregation.
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