Eigenvalue and Eigenvector Analysis of Dynamic Systems

While several methods aimed at understanding the causes of model behavior have been proposed in recent years, formal model analysis remains an important and challenging area in system dynamics. This paper describes a mathematical method to incorporate eigenvectors to the more traditional eigenvalue analysis of dynamic models. The proposed method derives basic formulas that characterize how a change in link (or loop) gain influence state behavior in linear dynamic systems. Based on the insights developed from linear theory, I extend the method to nonlinear dynamic systems by linearizing the system at every point in time and evaluating the impact to the derived formulas. The paper concludes with an application of the method to a linear system.