  We explore the coherent dynamics in a small network of three coupled
parametric oscillators and demonstrate the effect of frustration on the
persistent beating between them. Since a single-mode parametric oscillator
represents an analog of a classical Ising spin, networks of coupled parametric
oscillators are considered as simulators of Ising spin models, aiming to
efficiently calculate the ground state of an Ising network - a computationally
hard problem. However, the coherent dynamics of coupled parametric oscillators
can be considerably richer than that of Ising spins, depending on the nature of
the coupling between them (energy preserving or dissipative), as was recently
shown for two coupled parametric oscillators. In particular, when the
energy-preserving coupling is dominant, the system displays everlasting
coherent beats, transcending the Ising description. Here, we extend these
findings to three coupled parametric oscillators, focusing in particular on the
effect of frustration of the dissipative coupling. We theoretically analyze the
dynamics using coupled nonlinear Mathieu's equations, and corroborate our
theoretical findings by a numerical simulation that closely mimics the dynamics
of the system in an actual experiment. Our main finding is that frustration
drastically modifies the dynamics. While in the absence of frustration the
system is analogous to the two-oscillator case, frustration reverses the role
of the coupling completely, and beats are found for small energy-preserving
couplings.
