Analytical and Computational Methods for Analyzing Feedback Structure in System Dynamics Models

Abstract

The system dynamics approach is based on the observation that dynamic behaviour arises as a result of endogenous interactions, particularly the interplay of various feedback loops. There are many open questions relating to the relationship between system structure and its behavior, and there are opportunities to add to the range of formal mathematical methodologies which can identify dominant feedback structures that give rise to the system behavior. The objective of this thesis is to propose methodologies that can identify the structural origins of complex behavior, and investigate their application in system dynamics models. Our contributions to the field are: First, we have found a drawback of a widely adopted loop selection algorithm named SILS which is required by the eigenvalue elasticity analysis to identify dominant loops. We propose a specific algorithm is to address this problem, and demonstrate its applicability through an individual-oriented example. Second, with an increasingly emphasis on the study of eigenvector, an analytic eigenvector analysis method is proposed. As is known that, besides eigenvalue, the eigenvector plays an important role in determining the system behaviour as well. We develop an analytical approach, and suggest considering that both eigenvalue and eigenvector could provide an overall assessment of a structural change over the behaviour of interest. Third, for the behavioural method we first propose a new loop deactivation method which enables the behavioural method to operate even when no unique edge exists in a candidate loop. An example is provided to validate this method by comparing its analysis results with that from eigenvalue analysis. The introduction of this loop deactivation method makes the original method more robust and extends its applicability. Fourth, we propose an alternative criteria by measuring the sensitivity from different loops. We name this as the variant of the behavioural method. A series of testing values are used for each control variable in multiple simulations, and various trajectories of the variable of interest are obtained. The sensitivity from each loop thus can be measured. We hope by blending the sensitivity measurement, the behavioural method can be examined from another perspective and possibly more insights are gained. Finally, an extensive software library which automates the behavioural method and further has potential to implement its variant method has been designed and developed.