Previous work shows that auto-ignition propagation modes for strong knocking in engines are dominated by both chemical reactivity and energy density. To clarify the unique role of energy density and chemical reactivity, hotspot auto-ignition induced reaction wave propagation was investigated using direct numerical simulations, addressing the detonation regime in the detonation peninsula. Different operating conditions and mixture components were employed to design specific chemical reactivity and energy density under engine-relevant conditions. Various auto-ignition propagation modes were quantitatively investigated. The results show that unified standards for detonation development and high-accuracy excitation time are necessary for constructing a detonation peninsula. Energy density promotes detonation development and broadens the detonation regime, especially at large hotspot sizes. Meanwhile, there are positive correlations between peak pressure and energy density during detonation development, and the pressure peak can reach an amplitude beyond detonation equilibrium pressure. Furthermore, the improvement in chemical reactivity suppresses detonation development at small hotspot sizes while promoting detonation development at large hotspot sizes. But the variations in chemical reactivity caused by thermal effects show a greater significance than by fuel properties. Besides, obvious distinctions in peak pressure can be identified with the variations of reactivity gradient, and the amplitude always attains the maximum level just when detonation occurs at the edge of the hotspot. Underlying reasons are ascribed to the initial non-uniform distribution of energy density within the hotspot. Meanwhile, the reactivity progress of the remaining mixtures also affects energy density outside the hotspot.