  The response of a tunable photonic oscillator, consisting of an Optically
Injected Semiconductor Laser, under an injected Frequency Comb is considered
with the utilization of the concept of the Time Crystal that has been widely
used for the study of driven nonlinear oscillators in the context of
mathematical biology. The dynamics of the original system reduce to a radically
simple one-dimensional circle map with properties and bifurcations determined
by the specific features of the Time Crystal fully describing the phase
response of the limit cycle oscillation. The circle map is shown to accurately
model the dynamics of the original nonlinear system of ordinary differential
equations and capable for providing conditions for resonant synchronization
resulting to output frequency combs with tunable shape characteristics. Such
theoretical developments can have potential for significant photonic signal
processing applications.
