We study the dynamics of coupled oscillator networks with higher-order
interactions and their ability to store information. In particular, the fixed
points of these oscillator systems consist of two clusters of oscillators that
become entrained at opposite phases, mapping easily to information more
commonly represented by sequences of 0's and 1's. While 2N such fixed point
states exist in a system of N oscillators, we find that a relatively small
fraction of these are stable, as chosen by the network topology. To understand
the memory selection of such oscillator networks, we derive a stability
criterion to identify precisely which states are stable, i.e., which pieces of
information are supported by the network. We also investigate the process by
which the system can switch between different stable states when a random
perturbation is applied that may force the system into the basin of attraction
of another stable state