Applicability of the Homotopy Method to the determination of fixed points in chemical kinetics models

Reducing the complex chemical kinetics is an important challenge to implement chemical schemes in a turbulent combustion code. An important step in the reduction of chemical kinetics is to extract the fixed points of the set of differential equations associated with the chemical scheme since they are useful to determine the low manifolds which may be used to reduce kinetic mechanisms. This paper aims at testing a potentially powerful method, namely the Homotopy Method, for extracting fixed points from nonlinear dynamical systems. The method is tested on a 3D and a 7D model of the well-known Belousov-Zhabotinskii reaction. This study shows that the Homotopy Method has a significantly better efficiency than available Newton-Raphson algorithms but that the stiffness of the chemical kinetics equations still resists this method when the number of species increases