Behavior Modes, Pathways and Overall Trajectories: Eigenvector and Eigenvalue Analysis of Dynamic Systems

System Dynamics Review 25(1): 35-62, 2009

MIT Sloan Research Paper No. 4703-08

30 Pages Posted: 10 May 2008 Last revised: 8 Aug 2013

See all articles by Paulo Gonçalves

Paulo Gonçalves

Institute of Management, Università della Svizzera italiana (USI, Lugano); Massachusetts Institute of Technology (MIT) - Sloan School of Management - Operations Management and System Dynamics

Date Written: May 1, 2008

Abstract

One of the most fundamental principles in system dynamics is the premise that the structure of the system will generate its behavior. Such philosophical position has fostered the development of a number of formal methods aimed at understanding the causes of model behavior. To most in the field of system dynamics, behavior is commonly understood as modes of behavior (e.g., exponential growth, exponential decay, and oscillation) because of their direct association with the feedback loops (e.g., reinforcing, balancing, and balancing with delays, respectively) that generate them. Hence, traditional research on formal model analysis has emphasized which loops cause a particular "mode" of behavior, with eigenvalues representing the most important link between structure and behavior. The main contribution of this work arises from a choice to focus our analysis in the overall trajectory of a state variable - a broader definition of behavior than that of a specific behavior mode. When we consider overall behavior trajectories, contributions from eigenvectors are just as central as those from eigenvalues. Our approach to understanding model behavior derives an equation describing overall behavior trajectories in terms of both eigenvalues and eigenvectors. We then use the derivatives of both eigenvalues and eigenvectors with respect to link (or loop) gains to measure how they affect overall behavior trajectories over time. The direct consequence of focusing on behavior trajectories is that system dynamics researchers' reliance on eigenvalue elasticities can be seen as too-narrow a focus on model behavior - a focus that has excluded the short term impact of a change in loop (or link) gain in its analysis.

Keywords: Formal model analysis, overall trajectories, behavior modes, eigenvectors, eigenvalues, eigenvalue elasticity, loop dominance, behavior contribution

Suggested Citation

Gonçalves, Paulo, Behavior Modes, Pathways and Overall Trajectories: Eigenvector and Eigenvalue Analysis of Dynamic Systems (May 1, 2008). System Dynamics Review 25(1): 35-62, 2009; MIT Sloan Research Paper No. 4703-08. Available at SSRN: https://ssrn.com/abstract=1131392 or http://dx.doi.org/10.2139/ssrn.1131392

Paulo Gonçalves (Contact Author)

Institute of Management, Università della Svizzera italiana (USI, Lugano) ( email )

Via Giuseppe Buffi, 13
Lugano, CH-6904
Switzerland
+41 (0)58 666 44 79 (Phone)
+41 (0)58 666 46 47 (Fax)

HOME PAGE: http://web.mit.edu/~paulopg/www/

Massachusetts Institute of Technology (MIT) - Sloan School of Management - Operations Management and System Dynamics ( email )

30 Wadsworth St. E53-339
Cambridge, MA 02142
United States

HOME PAGE: http://web.mit.edu/~paulopg/www/

Register to save articles to
your library

Register

Paper statistics

Downloads
175
Abstract Views
1,338
rank
171,334
PlumX Metrics