  Ising machines (IM) have recently been proposed as unconventional
hardware-based computation accelerators for solving NP-hard problems. In this
work, we present a model for a time-multiplexed IM based on the nonlinear
oscillations in a delay line-based resonator and numerically study the effects
that the circuit parameters, specifically the compression gain $\beta_r$ and
frequency nonlinearity $\beta_i$, have on the IM solutions. We find that the
likelihood of reaching the global minimum -- the global minimum probability
(GMP) -- is the highest for a certain range of $\beta_r$ and $\beta_i$ located
near the edge of the synchronization region of the oscillators. The optimal
range remains unchanged for all tested coupling topologies and network
connections. We also observe a sharp transition line in the ($\beta_i,
\beta_r$) space above which the GMP falls to zero. In all cases, small
variations in the natural frequency of the oscillators do not modify the
results, allowing us to extend this model to realistic systems.
