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Setting: I have a single dataset from a simulation that appears to demonstrate bimodality. The dataset is composed of N measurements calculated at n different times and is two dimensional (N by n). At time $t_{end}$ the data visually appears to be bimodal. At time $t_{start}$, the data is drawn from a single distribution (initial conditions set by me). From $t_{start}$ to $t_{end}$ the system interacts in a complex manner to end up looking bimodal. No part of the final distribution looks anything like the initial distribution.

Problem: I believe the bimodality is hinting at two distinct populations that underwent different dynamical evolution during the course of the simulation. I would like to verify the bimodality and split the final dataset into two different populations in a statistically rigorous manner. How do I go about doing this?

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