  The impact of rotation on the bio-convective instability in a phototactic
algal suspension is investigated through a linear stability analysis in this
article. The study primarily focuses on the suspension's phototactic behavior,
which refers to the movement of microorganisms towards or away from light. In
conditions of low light, microorganisms exhibit positive phototaxis, moving
towards the light source, whereas in intense light, they display negative
phototaxis, moving away from the light source. The study specifically examines
a suspension that is illuminated by collimated flux, with a constant radiation
intensity applied to the top surface. The stability analysis is conducted
through the implementation of linear perturbation theory, which enables the
prediction of both stationary and oscillatory characteristics of the
bio-convective instability at the onset of biocnvection. It is observed that
rotation plays a significant stabilizing role in the system.
