AN INTRODUCTION TO SYSTEM DYNAMICS

    compiled by Paul Newton

System dynamics in brief

System Dynamics can be described by a simple Bathtub analogy

Stocks and Flows are the Origin of Dynamic Behavior (Change-Over-Time)

System Dynamics is used to help us Design Improved Social Systems

System Dynamics can model Desires, Expectations, Perceptions, and Goals

System Dynamics is typically used to produce Conditional, Imprecise Projections of Dynamic Behavior Modes

System Dynamics Models have specific advantages over Mental Models & The Success of System Dynamics Models must be measured against the Mental Models that would otherwise be used

Examples of System Dynamics Models developed to improve understanding of social systems

System Dynamics helps us discover Counterintuitive Behaviors of Social Systems & System Dynamics is, by definition, a Sustainability Tool

Introductory system dynamics papers on the internet & System dynamics in K-12 education papers on the internet

Endnotes and References

System dynamics in brief 

First, "system dynamics is a method for studying the world around us."[ii]  It helps us better understand the causes of interesting or surprising behavior, whether social, technological, or both.

Second, system dynamics helps us to find solutions to persistent problems.  If the behavior under study is not only interesting or surprising, but also undesirable, system dynamics can be used to find ways to improve that behavior. 

System Dynamics can be described by a simple Bathtub analogy 

Donella Meadows (1997)[iii] provides a very concise introduction to system dynamics: 

                        "To explain numbers, stocks, delays, flows, feedback, and so forth, I need to start with a basic diagram.

                        "The 'state of the system' is whatever standing stock is of importance-amount of water behind the dam, harvestable wood in the forest, people in the population, money in the bank, whatever.  System states are usually physical stocks, but they could be non-material ones as well - self-confidence, trust in public officials, perceived safety of a neighborhood.

                        "There are usually inflows that increase the stock and outflows that decrease it.  Deposits increase the money in the bank; withdrawals decrease it.  River inflow and rain raise the water behind the dam; evaporation and discharge through the spillway lower it.  Political corruption decreases trust in public officials; experience of a well-functioning government increases it.

                        "Insofar as this part of the system consists of physical stocks and flows - and they are the bedrock of any system - it obeys laws of conservation and accumulation.  You can understand its dynamics readily, if you can understand a bathtub with some water in it (the state of the system) and an inflowing faucet and outflowing drain (See Figure 1).   If the inflow rate is higher than the outflow rate, the stock gradually rises.  If the outflow rate is higher than the inflow, the stock goes down.  The sluggish response of the water level to what could be sudden twists of input and output valves is typical - it takes time for flows to accumulate.

                        "The rest of the diagram is information that causes the flows to change, which then cause the stock to change.  If you're about to take a bath, you have a desired water level in mind.  You plug the drain, turn on the faucet and watch until the water rises to where you want it (until the discrepancy between the desired and the actual state of the system is zero).  Then you turn the water off.

       

Figure 1:  Bathtub System

"If you start to get in the bath and discover that you've underestimated your volume and are about to produce an overflow, you can open the drain, until the water goes down to your desired level.

"Those are two negative feedback loops, correcting loops, one controlling the inflow, one controlling the outflow, either or both of which you can use to bring the water level to your goal.  Notice that the goal and the feedback connections are not visible.  If you were an extraterrestrial trying to figure out why the tub fills and empties, it would take a while to realize that there's a goal and a discrepancy-measuring process going on within the creature manipulating the faucets.  But if you watched long enough, you could figure that out. 

"Now let's take into account that you have two taps, a hot and a cold, and that you're also adjusting for another system state - temperature.  Suppose the hot inflow is connected to a boiler way down in the basement, four floors below, so it doesn't respond quickly.  And the inflow pipe is connected to a reservoir somewhere, which is connected to the planetary hydrological cycle.  The system begins to get complex and interesting.

"Mentally change the bathtub into your checking account.  Write checks, make deposits, add a faucet that dribbles in a little interest and a special drain that sucks your balance even drier if it ever goes dry.  Attach your account to a thousand others and let the bank create loans as a function of their combined deposits, link a thousand banks into a federal reserve system - and you begin to see how simple stocks and flows, plumbed together, make up systems way to complex to figure out."

Summarizing, system dynamicists believe that change is caused by the influence of a system's states on the actions that change those states. Differences between a desired state and an actual state cause actions intended to reduce the difference between the desired state and the actual state. However, actions intended to alter a state often alter other states as well, such that the consequences resulting from the action may not result in the desired states. This leads to a new set of actual and desired states, based on which further action is taken…..ad infinitum. The term feedback is used for this situation, in which a state causes an action that influences the initial state, either directly, or through intervening states and actions.  System dynamicists usually use the terms stocks and flows (or, alternatively, levels and rates) to represent, respectively, the states and actions within a system.  

System dynamicists usually use the terms stocks and flows (or, alternatively, levels and rates) to represent, respectively, the states and actions within a system. 

Stocks and Flows are the Origin of Dynamic Behavior (Change-Over-Time)

 

The bathtub system that Donella graphically portrays in Figure 1 could be represented in a system dynamics stock/flow diagram as in Figure 2.  A comparison of the actual depth of the water in the bathtub with the desired depth of water in the bathtub causes the user to alter the water flow into the bathtub via adjustments to the faucet, which, in turn, alters the actual water level in the bathtub.

Figure 2: A system dynamics stock/flow diagram representation of the Bathtub System from Figure 1

More complex systems, such as the ones described toward the end of  the excerpt from  Donella's writing, could be represented in system dynamics' stock/flow diagrams similar to Figure 3.  Looking at Figure 3, system dynamics posits that changes in systems (social and technological) occur when the levels of the stocks (the "system states", in the boxes) create changes in the flows (the valves, represented by valve symbols and double-lined "pipes"), which then act to change the stocks, ad infinitum.  (Note that the typical case is that a 'desired' state is itself a 'stock', and therefore subject to change via its own associated flows.) Therefore, a 'flow' could be a function of any number of 'stocks'. 

Figure 3: A more general stock/flow structure

 

For example, Donella mentioned that when filling a bathtub, how much we turn the hot and cold water faucets (flows) is influenced not only by how many inches of water we desire in the bathtub (one stock), but also by the final water temperature we desire (another stock).  Therefore, in this case, two stocks (water level and temperature) are influencing two flows (hot and cold water faucet positions), and sometimes a third flow (the drain - if the water is not at the right temperature when it reaches the desired height in the bathtub).  This system could be diagrammed as shown in Figure 4.  Note that there are six feedback loops in the system; can you identify them?

Figure 4: Bathtub stock/flow diagram considering both water level & temperature

System Dynamics is used to help us Design Improved Social Systems

Donella's last statement from her above quote, "you begin to see how simple stocks and flows, plumbed together, make up systems way too complex to figure out," is the reason that Jay Forrester[iv], among others, developed the discipline of system dynamics.  System dynamics is simple enough that it provides anyone with basic algebra skills a way to build models that describe to a computer how the pieces (stocks, and flows) of virtually any system, whether social, technological, or combined, fit together.  The computer can then trace the dynamic consequences of the interactions of those pieces as they influence one another over time, something that is very difficult for the un-aided human mind to do well, even for very simple systems.  Thus, system dynamics offers us the opportunity to use computers to help us design social systems in the same way that engineers have been using computers for decades to help them design technological systems. Given that today's engineers would not design a new technological product without using computer simulation, and given that social systems are much more complex than technological systems, we should take advantage of the discipline of system dynamics to help us design and improve social systems. 

System Dynamics can model Desires, Expectations, Perceptions, and Goals 

Another "distinguishing characteristic of the system dynamics paradigm is its emphasis on underlying causal mechanisms, whether directly observable or not, rather than on observed correlations.  In social systems models, any representation of causation must include human motivations.  System dynamicists are trained to be aware of and to include explicitly such factors as desires, expectations, perceptions, and goals [which are also system states - ed.]  Information about these behavioral factors is gained from social and psychological theory, from interviews with decision-makers in the system being simulated, and from observations of the actual decisions made under a variety of external circumstances."[v] 

System Dynamics is typically used to produce Conditional, Imprecise Projections of Dynamic Behavior Modes 

To perform its social system design assistance function, system dynamics must make predictions about the future.  But what is the nature of these predictions?  Dennis Meadows et. al. (1974)[vi] offers a concise answer:   

"To be useful to policy makers, a model must make some statement about the future, but information about the future may take several forms.  A model may provide, for example: 

1)                  Absolute, precise predictions. (Exactly when and where will the next solar eclipse be visible?)

2)                  Conditional, precise predictions.  (If the emergency core cooling system fails, what will be the maximum pressure on the nuclear reactor's containment vessel?)

3)                  Conditional, imprecise projections of dynamic behavior modes. (If corn prices are stabilized, will hog prices tend to fluctuate more or less strongly?)

4)                  Summary and communication of current trends, relationships, or constraints that may influence the future behavior of the system. (How do the paths of amino acid synthesis in a bacterial cell intersect?  Where does the town zoning plan allow commercial construction?)

5)                  Philosophical explorations of the logical consequences of a set of assumptions, without any necessary regard for the real-world accuracy or usefulness of those assumptions.  (On a curved surface, which theorems of Euclidean geometry still hold?  How many angels can dance on the head of a pin?)

 "[Most system dynamics models are] designed to provide information of the third sort… [This] level of knowledge is less satisfactory than a perfect, precise prediction would be, but it is still a significant advance over the level of understanding permitted by current mental models."

System Dynamics Models have specific advantages over Mental Models

&

The Success of System Dynamics Models must be measured against the Mental Models that would otherwise be used 

Using an urban dynamics context, Barney (1974)[vii] explains the relationships between mental and computer models, as well as some of the advantages of computer over mental models: 

                        "The urban system is an example of a 'complex system' - a system whose behavior is dominated by multiple-loop, nonlinear feedback processes.  Mathematical analysis is not very helpful in understanding complex systems since their nonlinear properties are as yet very difficult to treat analytically [this is still true in 1999 - ed.].  Currently the only successful method of dealing with systems as complex as the urban system is experimentation - with the actual system or with some representation of the actual system.  In the case of the urban system, most of the experimentation is done with a mental representation - the mental image (or model) we each have of how the urban system operates.

                        "Our public officials are constantly performing experiments with their mental models as they evaluate proposed changes and additions to laws and policies.  Although most public officials are probably not explicitly aware of it, their experiments involve three separate and distinct steps.  The official first brings to mind his latest mental image of how the system operates; he then uses his mental model to deduce the effects of the proposal; and finally he judges his deduction of the effects against his set of values and goals.  In the past, it has not been too important to distinguish these three steps, but as policy and legislative issues become more complex, it is increasingly important to know whether disagreements over a given proposal stem from different conceptions of how the system works, from inaccurate or inconsistent deductions of effects, or from more basic differences of values and goals.

                        "In turning to the computer for assistance, we are forced to consider each step separately.  Our mental image must be developed and expressed in a language that can be used to instruct the computer. Any consistent, explicit mental image of any system can be so expressed.  Our mental images are the results of our experiences and observations; formulating these experiences explicitly for the computer permits others to examine, correct, and comprehend our mental images and to contribute to a broader understanding through their different perspectives.  Given the expression of our mental images, the computer can point out inconsistencies, determine sensitivities, and deduce implications much more accurately than can the human mind - and without changing the ground rules part way along as the human mind is so prone to do. 

                        "But probably the most important contribution the computer makes is that it forces us to give separate consideration to questions of values and goals.  Given the implications of a proposed change in a law or policy, we are forced to ask if this is what we want, if this is consistent with our values, and if this brings us any nearer our collective goals.  With finite resources, cities can't be everything to everyone.  Given a better understanding of the options available and the effects of any given proposal, debate must then center on the desirability of the effects and the values necessary for judging desirability.

                        "By passing laws and changing policies, our public officials are making changes in the very structure of our society.  To assist in analyzing the questions they face, a model must not only reproduce the behavior of a city in a general sense; it must also correctly reflect the basic causal mechanisms at work within the city.  Many different models could potentially reproduce urban history, but a model that is to be used to examine the effects of change in policy must embody all of the important causal mechanisms - some of which are not yet easily measured or quantified.  This is a formidable requirement, and success for now must be measured not against an absolute standard of accuracy but rather against our only alternatives - inexplicit mental models or intuition." 

Examples of System Dynamics Models developed to improve understanding of social systems

To introduce system dynamics in a social system context, please read Jay Forrester'siv paper, Counterintuitive Behavior of Social Systems[viii].  This paper discusses applications of system dynamics to corporate, urban, and global sustainability problems.  Forrester provides a detailed example of a system dynamics model focused on the problem of global sustainability, showing how specific well-intentioned policies acting individually can produce counterintuitive and undesirable results for the world's human population and natural resource stocks.  Similar system dynamics-based social systems models have been and continue to be developed for specific needs in businesses, non-profit organizations, communities, cities, and countries[ix].

System Dynamics helps us discover Counterintuitive Behaviors of Social Systems

&

System Dynamics is, by definition, a Sustainability Tool

Forrester's paper viii also describes "three counterintuitive behaviors of social systems" that have been exposed via social system dynamics modeling, and which are "especially dangerous."  They are: 

1)                  "Social systems are inherently insensitive to most policy changes that people choose in an effort to alter the behavior of systems,

2)                  "Social systems seem to have a few sensitive influence points through which behavior can be changed," and

3)                  "Social systems [often] exhibit a conflict between short-term and long-term consequences of a policy change." 

A significant portion of sustainability activity is the search for policies in our social systems that will promote long-term, or 'sustainable,' consequences.  Indeed "…most system dynamics studies are concerned with the long term rather than the short term, and hence, they are all related to sustainable development, with an eye to seeking durable long-term gains."[x]  Therefore, 'long-term' is a synonym for 'sustainable'; that is, the very notion of sustainability involves finding and instituting policies that produce the best long-term consequences.   

System dynamics offers a tool to help us identify and communicate the rationale for those policies.  First, it helps us to collaboratively design sustainable social systems through use of models to identify sustainable policies and strategies.  Second, it helps us to more effectively communicate our designs to others.  Third, it helps others to better understand our designs, thereby enabling more reasoned dialogue in search of improved social systems.  System dynamics helps us to understand and therefore to endure the short-term negative consequences of sustainable policy decisions, giving us the patience to wait for the better long-term consequences that our modeling assures us are coming.  Because much system dynamics modeling involves a search for policies that give the best long-term consequences, system dynamics is by its very nature a sustainability tool.  

Introductory system dynamics papers on the internet

&

System dynamics in K-12 education papers on the internet

 Several papers are available at the bottom of the following web page: 

http://sysdyn.mit.edu/sd-intro/home.html 

The papers there are entitled: 

"The Beginning of System Dynamics",  

"Learning through system dynamics as preparation for the 21st century",  

"System dynamics meets the press", 

"System dynamics for kids", and  

"System Dynamics and Learner-Centered-Learning in Kindergarten through 12th Grade Education". 

Feel free to start anywhere, and read or review the titles that most appeal to you.  The papers are not in any sort of pre-requisite order. 

Once you are finished reviewing one or more of these papers, you may want to click on the "Road Maps: A Guide to Learning System Dynamics" link at the bottom of the above web page.  This carries you to the page: 

http://sysdyn.mit.edu/road-maps/home.html 

Once here, read this short page and click on the "table of contents" link toward the bottom.  This will take you to: 

http://sysdyn.mit.edu/road-maps/rm-toc.html 

There are several papers I'd like to recommend here.  Scroll down the page to Road Maps 1.  In Road Maps 1, you will see two papers that weren't in the above list.  They are entitled, 

"Simulating Hamlet in the Classroom", and  

"Counterintuitive Behavior of Social Systems"  

which last, as mentioned above, provides an excellent example of using system dynamics to learn about sustainability.   

From Road Maps 6, I recommend,  

"Systems thinking: critical thinking skills for the 1990s and beyond". 

For those of you who would like a general understanding of the system dynamics methodology for understanding change and finding ways to improve problematic dynamic behavior I recommend from Road Maps 7 and 8,respectively,  

"System dynamics, systems thinking, and soft OR", and 

"Building a System Dynamics Model Part 1: Conceptualization". 

Again, feel free to start anywhere, and read the titles that most appeal to you.  These papers are not listed in any specific order. 

If you have any questions, feel free to email or call mei. 

Endnotes and References

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