A simplified kinetic model for the tropospheric ozone cycle

Abstract

To better understand the dynamics of air pollutants, several mathematical or computational models have been developed and employed. Among the pollutants of interest are those related to the cycle of formation of tropospheric ozone (O₃), which involve nitrogen oxides NO_x. In this process, there is a sequence of chemical reactions whose most elementary modeling can be described in terms of ordinary differential equations (ODEs), in which the concentrations (in \textmu g/m³) of gases (O, NO, NO₂, and O₃) are functions of time. A novel study of the model is presented in terms of the qualitative theory of ordinary differential equations, for which the steady state of interest is non-hyperbolic. To study it, the Center Manifold Theorem was used to determine its stability. As for the results, our analytical calculations demonstrate the asymptotic local stability of the steady state, which was also numerically corroborated. Other than this new result of stability, the conclusion is that the simplified model of ozone kinetics with fixed kinetic parameters does not allow the behavior of sustained oscillatory solutions for the referred concentrations of pollutants, requiring other ingredients for this to be feasible.