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The linear stability of a suspension of isotropic scattering phototactic algae is investigated numerically with particular emphasis on the effects of Taylor number in the rotating medium. The suspension is illuminated by the oblique collimated irradiation. The solutions show a transition of the most unstable mode from stationary to an overstable state or vice versa for certain parameters at the variation in the Taylor number. Oscillatory instabilities are also observed at the three-quarter height of the suspension for some parameters.

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