Analytical properties and solutions of a modified Lindemann mechanism with three reaction rate constants

The present work provides an analytical treatment of a modified version of the Lindemann mechanism with three reaction rate constants. We firstly derive the exact analytical expressions among the three concentrations, then based on which the specific analytical forms of the invariant lines and feasible regions are also obtained, although the existence of the invariant lines has been proved in a recent work. An efficient semi-numerical and semi-analytical solution is also constructed in the framework of Piecewise differential transform method (PDTM). What is more, the reaction dynamical properties including the limiting behaviors are further discussed.