Limit combustion phenomena, such as ignition, are rather sensitive to chemical kinetics and these properties are therefore used to physically characterize the behaviour of different fuels. In the framework of bifurcation theory, the ignition and extinction phenomena for combustion occurring in a Perfectly Stirred Reactor correspond to saddle-node bifurcation points and leads to the classical S-shaped steady-state curve. Then, the location of ignition and extinction conditions and their dependence on the main parameters (like pressure, equivalence ratio, residence time or inlet temperature in reactors) can be reformulated as a problem of bifurcation analysis. Even when the reactive mixture is described by a simple surrogate, but in conjunction with very complex and detailed chemical mechanism, with several hundreds of species and thousands of chemical reactions, the computation of the bifurcation diagram becomes computationally very demanding. In this work we explore this issue. The several steps required to formulate a complete continuation algorithm are analysed from a computational point of view and convenient formulations or approaches are introduced to made viable this kind of analysis even adopting desktop class computers. It is shown that the adoption of a Broyden type corrector in the continuation algorithm outperform for this problem the usually adopted Newton type correctors. Consequently, we introduce a suitable algorithm to investigate ignition, extinction and linear stability of the air-fuel mixtures in PSR. The algorithm is based on the well-known Keller pseudo-arclenght continuation method in order to compute steady state solution curve. The solutions stability and then ignition and extinction states are identified by test functions based on the numerical eigenvalues of the Jacobian of the governing system of equations. The algorithm is implemented in the numerical computing environment Matlab coupled with the CANTERA Toolbox for managing of complex chemical kinetic mechanisms and species properties. The algorithm is thus easily applicable to chemical schemes available in the standard CHEMKIN format. To demonstrate the capability of the resulting method, the characteristic S-Shaped curve, including non-stable branches, for different Air-Jet Fuels mixtures have been computed.