<p>The distribution of exothermic reaction rates is jointly influenced by reduced activation energy and reaction rate constant. This study focuses on the effect of distribution of exothermic reaction rates on detonation wave propagation instability, specifically under conditions where the length of the induction and exothermic reaction remains constant. It is found that the distribution variation of exothermic reaction rates significantly influences the detonation wave propagation characteristics. Specifically, under conditions of high activation energy, the exothermic reaction rate profile exhibits a smoother distribution but becomes more prone to perturbations. This heightened sensitivity, coupled with the augmented overdriven degree associated with pulsating detonation and cellular detonation wave propagation, further exacerbates the instability characteristics of detonation waves. Especially to the two-dimensional detonation waves with high activation energies, the distribution of exothermic reaction rates becomes more sensitive to these displacements, reinforcing the transverse shock wave and leading to a transformation of the wavefront and cellular structure towards more unstable configurations. This research delves into the intricate interactions between the distribution of exothermic reaction rates and detonation wave instability, aiming to provide an explanatory of detonation instability.</p>