The paper introduces a numerical tool based on a predictor-corrector continuation algorithm to obtain the bifurcation analysis of a perfectly stirred reactor with detailed reaction mechanisms. Each step of the continuation algorithm is reviewed and adapted to handle reaction mechanisms with hundreds of species and thousands of reactions. Particularly, the adoption of a Broyden solver in the predictor-corrector algorithm and a new formulation of the test functions are proposed. The implementation in Matlab and the adoption of the CANTERA Toolbox, make the tool easily applicable to reaction mechanisms available in CHEMKIN format. To validate and demonstrate the capability of the tool, the full equilibrium curves have been obtained for three different cases, having increasing number of species and reactions: methane-air (GRIMech.1.2), simple surrogates of Jet-A in air (JetSurF2.0) and a ternary surrogate of Jet-A in air (CRECK). The tool gets performances that make affordable the computations even with desktop computers. (C) 2015 Elsevier Ltd. All rights reserved.