The shock front nonstationarity of perpendicular shocks in super-critical regime is analyzed by examining the coupling between incoming and reflected ion populations. For a given set of parameters including the upstream Mach number (MA) and the fraction α of reflected to incoming ions, a self-consistent, time-stationary solution of the coupling between ion streams and the electromagnetic field is sought for. If such a solution is found, the shock is stationary; otherwise, the shock is nonstationary, leading to a self-reforming shock front often observed in full particle simulations of quasi-perpendicular shocks. A parametric study of this numerical model allows us to define a critical αcrit between stationary and nonstationary regimes. The shock can be nonstationary even for relatively low MA(2--5). For a moderate MA(5--10), the critical value αcrit is about 15 to 20%. For very high MA (>10), αcrit saturates around 20%. Moreover, present full simulations show that self-reformation of the shock front occurs for relatively low ¿i and disappears for high ¿i, where ¿i is the ratio of upstream ion plasma to magnetic field pressures. Results issued from the present theoretical model are found to be in good agreement with full particle simulations for low ¿i case; this agreement holds as long as the motion of reflected ions is coherent enough (narrow ion ring) to be described by a single population in the model. The present model reveals to be at variance with full particle simulations results for the high ¿i case. Present results are also compared with previous hybrid simulations.