Oblique detonations induced by two-dimensional, semi-infinite wedges are simulated by solving numerically the reactive Euler equations with a two-step induction-reaction kinetic model. Previous results obtained with other models have demonstrated that for the low inflow Mach number M-0 regime past a critical value, the wave in the shocked gas changes from an oblique reactive wave front into a secondary oblique detonation wave (ODW). The present numerical results not only confirm the existence of such critical phenomenon, but also indicate that the structural shift is induced by the variation of the main ODW front which becomes sensitive to M-0 near a critical value. Below the critical M-0,M-cr, oscillations of the initiation structure are observed and become severe with further decrease of M-0. For low M-0 cases, the non-decaying oscillation of the initiation structure exists after a sufficiently long-time computation, suggesting the quasi-steady balance of initiation wave systems. By varying the heat release rate controlled by k(R), the pre-exponential factor of the second reaction step, the morphology of initiation structures does not vary for M-0 = 10 cases but varies for M-0 = 9 cases, demonstrating that the effects of heat release rate become more prominent when M-0 decreases. The instability parameter chi is introduced to quantify the numerical results. Although chi cannot reveal the detailed mechanism of the structural shift, a linear relation between chi and k(R) exists at the critical condition, providing an empirical criterion to predict the structural variation of the initiation structure. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.