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Show INTRODUCTION The dynamical system of equations for the Perfectly Stirred Reactor (PSR) to be presented in this paper, is an extension of the PSR equations proposed in the Baker and Essenhighl paper. The system presented in their paper, had only two variables, temperature and fuel concentration, which described a two dimensional first-order autonomous system. Our set of equations are expanded to include oxygen concentration as an additional time dependent variable. In this paper we will propose a new system of equations, and we will give the results of a bifurcation analysis that was performed on the new system. The Perfectly Stirred Reactor analysis was developed 3 to 4 decades ago, to help describe behavior at the ignition and extinction limits, and other characteristics such as pulsating behavior. It was a steady-state analysis, based on the Semenov TET approach, equating a line representing the heat loss with the sigmoid curve related to the heat generated. The extinction and ignition limits are determined by the points of tangency of the line with the sigmoid curve. Essentially it was shown that conditions outside the limits had only one steady-state solution near zero (near zero: room temperature and fuel consumption); and within the limits there were three solutions, one being the near zero solution2 • PSR analysis was also used to model engines with extremely high mixing, such as the jet engines analysised by Bragg3 , and the VI analysed by Avery and Hart4 . Then interest in the PSR declined in the following years, partly due to the emergence of: more sophisticated models, which included more complete use of the Navier Stokes equations; and computers that could solve the complicated models numerically. However, there has been a recent revival in PSR and other similar analysis, because of the development of bifurcation analysis. The essence of bifurcation analysis is to study the variation of the steady state solutions of the dynamical-system of equations and their stability as physical parameters 2 |