  Coupled nonlinear systems have promise for parallel computing architectures.
En route to realizing complex networks for Ising machines, we report an
experimental and theoretical study of two coupled parametric resonators
(parametrons). The coupling severely impacts the bifurcation topology and the
number of available solutions of the system; in part of the stability diagram,
we can access fewer solutions than expected. When applying noise to probe the
stability of the states, we find that the switching rates and the phase-space
trajectories of the system depend on the detuning in surprising ways. We
present a theoretical framework that heralds the existence of 'ghost
bifurcations'. These bifurcations involve only unstable solutions and lead to
avoided zones in phase space. The emergence of such ghost bifurcations is an
important feature of parametron networks that can influence their application
for parallel logic operations.
