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2013 | OriginalPaper | Chapter

8. Measuring the Degree of Dynamic Complexity in Differential Equation Simulation Models

Author : Stefan N. Grösser

Published in: Co-Evolution of Standards in Innovation Systems

Publisher: Physica-Verlag HD

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Abstract

Dynamic complexity is an important aspect of the realm of management. It is present, for instance, when an action has one set of consequences locally and a different set of consequences in another part of a system. Dynamic complexity can be captured and analyzed by ordinary differential equation models of the system dynamics type. Measuring such a model’s degree of dynamic complexity approximates the dynamic complexity of the modeled system. No approach exists, however, for measuring this concept. Here, the chapter contributes with three measures of dynamic complexity called DYCO, Fractional Durations, and Crude Model Structure. These measures yield several benefits: First, one can inspect the degree to which a quantitative model can capture the degree of dynamic complexity. Second, one can evaluate the property of such a model to endogenously generate its behavior. Third, these measures can be used to enhance the validity of simulation models. And finally, they can enliven discussions about dynamic complexity. The chapter develops these measures by means of a cascade of examples. Limitations and future research are discussed.

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Footnotes
1
A model output is a variable of interest in a simulation model. This is discussed in more detail in the Chapter 8.3.3. For instance, “inventory” is an example of an output variable of the inventory control model (Sterman, 2000, Chap. 15).
 
2
A behavior space is the collection of behaviors a system can follow.
 
3
The terms “balancing” and “reinforcing” do not indicate a direction or a sense of quality. I use them here as a description of the mathematical realities of the perceived mechanisms (for more details, see Sterman, 2000).
 
4
This is one of the axioms of system dynamics: system structure generates system behavior (Forrester, 1961; Saleh, 2000).
 
5
I thank Henry Weil, Sloan School of Management, Massachusetts Institute of Technology, for bringing this to my attention.
 
6
The model are available upon request.
 
7
In stock and flow diagrams, a stock is represented as rectangular; a flow/transition function is shown as a double arrow including a value symbol (see Table 8.3; also Sterman, 2000).
 
8
Reaching an exact value of 0 is unlikely because of numerical integration and computations. To operationalize the zero-condition, a threshold is introduced which is a fraction of 3% of the maximum level which the BPI assumes in an individual simulation run. This assumption has been tested and is robust for large ranges of simulated behavior.
 
9
I start with Toy2. The model has only two exogenous inputs (time to adjust and goal) which are both independent of time. The application of DYCO to both results in a value of 0 due to the absence of any change. Toy1 has also two exogenous inputs (market share and market value), the first of which is independent of time and also results in a DYCO of 0. The latter depends on time and follows a constant linear growth which results also in a DYCO of 0. In both cases, the exogenous inputs do not bias the measure of the dynamic complexity of Toy1 or Toy2.
 
10
The measures developed here cannot explain which specific model structures dominate the trajectory of a stock at which times; this is the objective of loop dominance analysis. The changes of the dominant structure are obvious to the experienced analyst for this simple model. The same cannot be easily inferred for a more complex model, e.g., Repenning’s model (2002).
 
11
I have tested this with published models (Vancouver et al., 2005; Vancouver, Weinhardt, & Schmidt, 2010) which make use of the discrete functions of Vensim©. The measures overestimate the number of shifts in feedback dominance, due to the abrupt changes which discrete functions introduce.
 
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Metadata
Title
Measuring the Degree of Dynamic Complexity in Differential Equation Simulation Models
Author
Stefan N. Grösser
Copyright Year
2013
Publisher
Physica-Verlag HD
Book
Co-Evolution of Standards in Innovation Systems

Print ISBN: 978-3-7908-2857-3

Electronic ISBN: 978-3-7908-2858-0

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-7908-2858-0_8