Large pressurized power reactors (PWR) are subject to spatial instabilities. Such instabilities usually rise due to delayed negative feedbacks of fission products, mainly by the formation of iodine and xenon, which may yield spatial and temporal oscillations. We apply the formalism of pattern formation in nonequilibrium physics to study these oscillations. The dynamics are described using a nonlinear model, which includes feedback processes of both fission products and temperature. We show that the homogeneous solutions are unstable to Hopf bifuracation in multiple regions of the bifurcation parameter's values which correlate to various regions of the flux values. Moreover, under non-uniform perturbations, there exists a range of wavenumbers for which a standard PWR reactor is unstable through periodic oscillations. The Hopf bifurcation is further investigated upon applying the tools of multiple time scales perturbation theory on the model, resulting in a better understanding of the phenomenon and the typical time scales of the instability.