A Comprehensive Eigenvalue Analysis of System Dynamics Models

Abstract

In this paper, we develop a comprehensive eigenvalue analysis for linear models, in order to identify the leverage points in models. The analysis is comprehensive as we develop a closed-form analytic function relating the behavior of any state variable to all parameters in the model. Moreover, by decomposing the behavior into several modes of behavior – each characterized by an eigenvalue and an eigenvector – it is possible to develop a closed-form analytic function relating a certain mode of behavior to all parameters in the model. In the first section of this paper, we explain the mathematical foundation of eigenvalue analysis. In the second section we identify the origin of the modes of behavior. This enables us to pinpoint the leverage points of the model. Finally, in the last section, for illustration purpose, we apply the method to a linearized version of the classical market growth model. The analysis of this linearized model enables us to explain the model behavior as a superposition of a number of behavior modes, and set the stage for analyzing the original, non-linear version of the model.