ABSTRACT
Analysis of nonlinear systems is a vast and important field. A nonlinear system displays a very rich repertoire of interesting dynamics. Any nonlinear system can be analyzed in the vicinity of a steady state by linearizing it and computing its eigenvalues to predict is dynamic behavior near the steady state. Additionally, linear system analysis provides an extremely powerful tool to analyze a general n-dimensional system. The discussion on the dynamics of a linear system of ordinary differential equation (ODEs) focused on the effect of eigenvalues on the system dynamic behavior. The eigenvalues determine the asymptotic or long-time behavior of the system. Eigenvalues with negative real parts indicate stable response. Analysis of reactors with strong temperature effects can indeed be done by solving mass and energy balances for the plug flow reactor (PFR) simultaneously. However, at times, detailed analysis or parameter estimation in the presence of local temperature trends calls for an approach to decouple temperature and mass balance effects.
