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Combustion modes in locally stratified dual-fuel (DF) mixtures are numerically investigated for methanol n-dodecane blends under engine-relevant pressures. In the studied constant-volume numerical setup, methanol acts as a background low-reactivity fuel (LRF) while n-dodecane serves as high-reactivity fuel (HRF), controlling local ignition delay time. The spatial distribution of n-dodecane is modeled as a sinusoidal function parametrized by stratification amplitude (Y) and wavelength (0.01 mm<$λ$<15 mm). In contrast, methanol is assumed to be fully premixed with air at equivalence ratio 0.8. First, one-dimensional setup is investigated by hundreds of chemical kinetics simulations in (Y,$λ$) parameter space. Further, the concepts by Sankaran et al. 2005 and Zeldovich 1980 on ignition front propagation speed are applied to develop a theoretical analysis of the time-dependent diffusion-reaction problem. The theoretical analysis predicts two combustion modes, 1) spontaneous ignition and 2) deflagrative propagation, and leads to an analytical expression for the border curve called $β$-curve herein. One-dimensional chemical kinetics simulations confirm the presence of two combustion modes in (Y,$λ$) parameter space while the $β$-curve explains consistently the position of phase border observed in the simulations. Finally, the role of convective mixing is incorporated to the theoretical expression for the $β$-curve. The effect of convection on combustion mode is assessed by carrying out two-dimensional fully-resolved simulations with different turbulence levels. Two-dimensional numerical simulation results give evidence on combustion mode switching, which is consistent with predictions of the modified $β$-curve for turbulent cases. The practical output of the paper is the $β$-curve which is proposed as a predictive tool to estimate combustion modes ...