A bifurcation analysis was developed to systematically detect limit flame phenomena, including ignition, extinction and changes in flame stability, and to understand the underlying physicochemical processes that control the limit phenomena. The bifurcation analysis was demonstrated with steady-state perfectly stirred reactors (PSRs) using dimethyl ether (DME) with the negative temperature coefficient (NTC) chemistry. Flame stability was first analyzed to identify ignition and extinction states based on the eigenvalues of the Jacobian of the governing equations. It was found that for DME-air mixtures, extinction may not occur at the turning points on the S-curves. A bifurcation index (BI) was then defined at each bifurcation point on the S-curves to quantify the contribution of each reaction and the mixing process to the limit flame phenomenon. Results show that extinction of the strong flames of DME-air is primarily controlled by the reactions involving small molecules, such as HCO and CO, while extinction of the cool flames is primarily controlled by the NTC chemistry involving larger molecules. To validate this method, the pre-exponential "A"-factors of the selected reactions were perturbed. It was found that the perturbations in reactions with large BI values have significant effects, while those with small BI values have minor effects, on the ignition and extinction states. The BI-based method was further compared to sensitivity analysis, and overall-consistent results were observed on the importance of the reactions at the bifurcation points, indicating that the bifurcation analysis is effective in identifying controlling reactions for limit flame phenomena. The BI values were then employed to guide the refinement of the rate constants in the DME mechanism. A skeletal model with substantially reduced reaction set and systematically tuned rate constants was obtained to accurately capture both steady-state and transient ignition and extinction behaviors of DME-air in PSR. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.