Introduction to Systems and Modeling

Part 1: Introduction

There is a quiet revolution taking place in the sciences. Like all revolutions, it started small and has grown in size and importance since its inception. With every year, it grows more central in our lives, shaping everything about our experiences from driving to shopping, working to making friends. It allowed us to get to the moon. It made the difference in World War II. It’s enabling us to make ground in the battle with cancer, and gives us the power to predict the trajectory of ongoing climate change. What is this revolution?

The answer is deceptively simple: computers. Look back at the list of examples above. How are computers involved in all of them? Most importantly, how have computers enabled us to tackle problems once impossibly out of reach due to their complexity? Could we have gotten to the moon without computers? It seems unlikely!

A key moment in the journey towards powerful computers was World War II, a conflict of unprecedented horror and scale that placed enormous pressure on science and technology to provide an advantage. Some of the most historic battles were fought not in the field, but at England’s Bletchley Park, where mathematicians and engineers engaged in an intellectual struggle to crack Enigma, a seemingly unbreakable code used by the Germans. In collaboration with England’s greatest minds, brilliant mathematician Alan Turing developed a machine, The Bombe, to run through thousands of possible keys to identify the correct one for each day’s code. The coded messages cracked thanks to insights derived from this machine helped the Allies win the war. The Bombe was not technically a computer - it could only carry out its one purpose and could not be adapted for another use with different software. But it was a harbinger of things to come. A thorny problem, with massive quantities of data and possibilities to test, was only solvable by the help of a machine.

Many problems are beyond the human mind due to their scale and complexity. Have you ever used Google Maps to guide your way through rush hour in a dense metropolitan area? Behind the slick interface and calm route suggestions, algorithms are churning through millions of data points - cars on the road, their speeds and locations, their dynamics at key traffic bottlenecks, construction and accidents, and how all of these elements are changing with time. No human mind could handle this onslaught. Much like Enigma, a problem that is easy to understand - what is the correct key to translate these messages? What is the fastest route to my destination? - is made inaccessible by vast quantities of data. Enter the computer.

Most of us use computers as smart typewriters, big file cabinets, fast mail services or slow telephones, and very large libraries. But that is not their real power. Their real power is that they allow us to think in a way that has never before been possible. Computers allow us to address the complexities of the world. Modern science is faced with a world in which the simplest problems have been answered. The most urgent, and most difficult, questions invariably deal with large systems, consisting of many parts interacting in complex ways. Climate change is a vast system, involving layers and layers of subsystems with billions of moving parts and connections. Medical science faces similarly complex systems in the form of human bodies and the diseases that afflict them. The only realistic way to tackle these big questions is by taking advantage of computers. Computers could never handle these problems on their own. But they are an invaluable tool for the scientists working on these problems today.

On this page, we are going to explore the nature of systems. You will see how even the most complex systems have underlying structures that can be understood and used to identify principles that apply to many seemingly different systems. You will come to appreciate the magnitude of the challenge, and learn how computers can help us make models of these systems that will help us understand them better and answer the great questions of today.

Part 2: Shifting from Traditional Science to Systems Thinking

Traditional Lab Science is Reductionist

We are very good at figuring out if “A” causes “B”. The determination of this relationship is the basis for traditional laboratory science. Experiments are designed to reduce a question to a single causal relationship between whatever “A” and “B” we are interested in. This approach is reductionist because it tries to isolate cause and effect, simplifying an otherwise intractably complex problem. Reductionist science is a powerful tool that has lifted mankind from the Neolithic, stone-age to the present day. It remains extremely effective and impactful. In the nineteenth century, it took about fifty years to double the world's knowledge. Today, our knowledge doubles in less than a year.

Ray Kurzweil of Google writes, “An analysis of the history of technology shows that technological change is exponential, contrary to the common-sense “intuitive linear” view. So we won’t experience 100 years of progress in the 21st century — it will be more like 20,000 years of progress (at today’s rate). The “returns,” such as chip speed and cost-effectiveness, also increase exponentially. There’s even exponential growth in the rate of exponential growth. Within a few decades, machine intelligence will surpass human intelligence, leading to The Singularity — technological change so rapid and profound it represents a rupture in the fabric of human history. The implications include the merger of biological and nonbiological intelligence, immortal software-based humans, and ultra-high levels of intelligence that expand outward in the universe at the speed of light.”


Wicked Problems

However, as humans expand to the limits of the globe, a series of issues have arisen that are known as “wicked problems”. The issues range in size and complexity from climate change to the opioid crisis, but what they have in common is that understanding and solutions are not found in simple, single causal relationships. Instead, they are the result of multiple, complex, interacting, causal loops that together create systems. This sort of situation does not lend itself to traditional experimental design or observation.

In order to tackle these “wicked problems,” we need to understand systems as objects themselves, with their own characteristics, behaviors, and opportunities to effect change and find solutions. Instead of reducing a complex system to its component parts, we need to take a step back and look at systems in their entirety - to the best of our ability.

So what are systems? How can we understand and work with them?

Part 3: Systems Thinking: Negative and Positive Feedback Loops (Draper L. Kauffman, Jr.)

An Introduction to Systems Thinking

In 1980, Draper L. Kauffman, Jr. wrote an educational series titled “Systems” that explains the underlying structures of systems with the help of charming illustrations with birds. Even 40 years later, his lessons provide great insight into the nature of systems. The following section draws heavily from the first chapter, “Systems One: An Introduction to Systems Thinking.” A PDF copy of the full chapter can be downloaded for free from All quotes and images are the property of Dr. Kauffman.

Systems within Systems

A system is a collection of parts which interact with each other to function as a whole.

Examine this definition of a system and think of some examples of systems in the world. Think big and small. In your examples, what are the “parts” of the system? How do they “interact”? What is the larger “function” of the system?

In some of your examples, you may have noticed that some of the component “parts” are themselves a system. For example, the world’s climate is a vast system made up of many subsystems, such as oceans, landmasses, the atmosphere, human beings, plants, and so on. Most systems will fall somewhere on a hierarchy of systems, as you can see in the diagram.

Kauffman says, “Each system on the list combines with other systems of about the same level to make up the next larger system. Thus a particular protein molecule might contain atoms of carbon, hydrogen, oxygen, and nitrogen.

Why is this true? If you stop to think about it, this neat progression of steps, from the smallest particle up to the entire universe, does seem rather odd. Why doesn’t nature just make larger particles, instead of building atoms up out of small ones? Why not just have larger and larger atoms, instead of building molecules up from combinations of atoms? For that matter, why are you composed of many billions of cells instead of being one super-giant-sized cell?

It seems that the reason in every case is that a collection of smaller units - a system - is more stable than one large unit. A cell larger than a certain size would simply die of suffocation, unable to move oxygen and food in, or waste products out, fast enough to stay alive.

It is easy to see how this works with social organizations. A group of five people can work together as a single team, but a group of five thousand people would find it almost impossible to get anything done without dividing up into smaller working groups and organizing some way of communicating between those groups. In other words, a group that big is just a disorganized crowd or mob unless one or more higher levels of system organization are created.”

Negative feedback loops provide stability to systems

Why are systems stable? To answer this question, Kauffman returns to his definition of a system: “A system is a collection of things which interact with each other to function as a whole. The key word here is ‘interact’. If one part has an effect on the rest of the system and the system as a whole has an effect on that one part, then a “circular” relationship - or “loop” - has been created.

For example, you and a bicycle together form a simple, two-part system. Combined, you can do things which neither you nor the bicycle can do separately. Furthermore, your actions have an influence on what the bicycle does and the behavior of the bicycle has an influence on your actions.

Now, the interesting thing about even such a simple system as this one is the way it creates stability out of a situation which would normally be very unstable. If you climb on the bike and do nothing, neither you nor the bike will stay upright very long.”

When you ride the bike, your brain receives “input” in the form of signals from the environment that you use to decide what you’re going to do - start pedaling, turn, use the brakes, etc. The “output” is the motion of you and the bicycle together. However, the output creates new information that your brain receives as new “input” - your bike is in a new location, and perhaps you need to turn or change your action in some other way.

Kauffman continues, “In this way, information about the output of the system is fed back around to the input side of the system. Information that is used this way is called feedback, and any system like the one diagrammed above is called a feedback loop.

Can you now see how this feedback provides stability in a system that would otherwise be unstable? Because this kind of system acts to cancel out or negate any changes in the system, it is called a negative feedback loop. This idea of negative feedback seems simple but it is extremely important for understanding the systems in our environment.

Unfortunately, the phrase “negative feedback” is sometimes used loosely as a synonym for “criticism,” particularly in education. When talking about systems try to keep in mind that negative feedback isn’t necessarily good or bad. It is simply a process which negates change or disturbances in the system.”

Negative feedback loops are everywhere. Here are some examples:

    • Thermostat

    • Body Temperature

    • Float Valves (in toilets and carburetors)

    • Thirst

    • Inventories (Law of Supply and Demand)

    • Predator-Prey Relationships

All of these loops are examples of negative feedback. When one element goes up, another goes down, and the ultimate result is to maintain the status quo. If the water content in your body drops too low, thirst signals are increased, so you drink water, which increases your water content and stops the thirst signals. The outcome is that your body maintains a healthy level of water for optimal function. Notice that this is a very “positive” outcome - it saves you from dying of thirst! The negative element comes from the system, in this case your body, preventing unwanted change by connecting different elements of the system together.

Positive feedback loops allow for change and growth in systems

“Negative feedback loops provide stability for the systems in our environment. How then do change and growth occur? … A great deal of change going on around us comes from a completely different kind of feedback process, called positive feedback.

Feedback occurs when a change in one part of a system produces changes in the whole system which then “feed back” through the system and affect the original part again. Negative feedback works to cancel out, or negate, changes. .. But what happens if the feedback loop does just the opposite, and each change feeds back through the system to cause more change? The new change will cause still more changes, and so on, until something breaks the cycle. This is called positive feedback because it amplifies or adds to any disturbance in the system.

An example is microphone-amplifier feedback. If a microphone gets too close to a speaker, sound enters the microphone, goes through an amplifier, leaves the speaker louder than it was, re-enters the microphone, leaves the speaker louder yet again, and so on, until the speaker lets out a deafening SQUAWK. This positive feedback cycle would continue forever, except someone usually yanks the microphone away, interrupting the loop.

Other examples of positive feedback:

  • Money - compounding interest (small scale); economic growth (large scale)

  • Population - cell division, births

  • Knowledge - knowledge begets more knowledge

  • Power - power begets more power

“The growth of knowledge, the growth of population, the growth of economic wealth, and the growth of power are the greatest forces of chance in modern life. Together, [they create] an unprecedented situation of rapid and continuous change. One of the basic challenges of our time is finding ways to control this headlong change.” This type of growth is often called exponential growth. For example, the number of transistors that can fit on a chip has increased exponentially in the last few decades, a rule known as Moore’s Law.

As you can see in the charming illustration below, knowledge also functions through a positive feedback loop, especially at a societal level - as a group of people gains useful knowledge, future generations of that group can build on the existing knowledge base and gain even more knowledge. This process has reached a fever pitch in our current era. Just think about what cell phones looked like in TV shows from the 90s!

"Positive feedback affects our lives in less general ways. The spread of a fire, a rumor, a chain letter, an epidemic disease - all of these are the result of positive feedback, as are all chemical and nuclear chain reactions. What they all have in common is an explosive quality, whereby a tiny initial spark can quickly cause enormous results. They are also often dangerous. As a result positive feedback loops are usually kept under very tight control in both natural and social systems."

Systems are made of positive and negative feedback loops in balance

“Only in the last [90 years] have people begun to realize that all complex systems have many things in common in the way they are organized, even though the ‘pieces’ may be very, very different.

The organization of every complex system is built out of the same two simple elements that we have just been discussing: positive and negative feedback loops.

This similarity gives us a powerful tool. Now that you understand the basic units of organization, you can hunt for them in any particular system and see the similarities between the way that system behaves and the way other systems behave.

An important example of the balancing effects of positive and negative feedback is population dynamics, particularly predator-prey relationships. Kauffman uses rabbit populations as an example, a notoriously fast-reproducing species. The positive feedback loop comes from births - the more rabbits there are, the more births there are. “On the other hand, as the population of rabbits increases, the number of rabbits that die each year also increases. This is the negative loop in the diagram.

The actual behavior of the system depends on which loop is ‘stronger’. If the birth rate is higher, the population will grow; if the death rate is higher, the population will decline. The same basic description applies to many other systems.” For example, the growth of knowledge in a society depends on the rate of discovery being greater than the rate of forgetting. When events happen that cause mass losses of knowledge - for example, the burning of the Library of Alexandria - knowledge accumulation is knocked back for a while until the positive feedback loop regains strength.

So what controls the rate at which the basic positive and negative feedback loops work? Many negative feedback systems are in place to keep the rates of positive and negative feedback in an appropriate balance. In the case of a rabbit population, such negative feedback systems include predator activity, food availability, disease, and space availability. These feedback systems may not all be in use at the same time, but rather some control the population under normal situations (e.g., predator activity), while others only take effect under extreme circumstances (e.g., overcrowding, if predator activity decreases for some reason).

Take a look at the diagram of a rabbit population and the factors affecting it. Imagine a specific situation and how it would affect the system. For example, what if there was a cold winter and the amount of food decreased sharply? The death rate would increase, causing a decrease in population, which causes a decrease in births.

However, the population decrease would cause an increase in space per individual, which could both decrease deaths and increase births. After some time the population would rebound to normal levels. In this way, the multiple negative feedback loops work to buffer changes in the system, bringing it back to a healthy status quo.

“This pattern is common in many types of systems, and often leads to frustration for people who are unfamiliar with the way systems normally behave. People often intervene in a system to eliminate a negative feedback loop that they don’t like, only to be surprised when a worse one takes its place. For example, if disease is reduced through better medicine and nothing is done to limit the birth rate, the human population then increases to the point where there is not enough food and a great famine occurs, killing even more people.

One of the first things to look for in any complex system is the nature of the positive and negative feedback loops and the relationship between them. Generally speaking, the point at which the positive forces and the negative forces balance each other is the point the system will go back to, time after time, after being disturbed by some change in its environment.”

Part 4: Types of Systems

Now that we understand some of the underlying structures of systems, we can begin to explore how scientists study them. With so many wicked problems rearing their heads, what is needed is a different sort of science - a science seeking repeating patterns in the world. For instance, what are the similarities between a cooling cup of coffee and last year’s flu outbreak at your school? Do the coffee cup’s temperature and the number of sick students illustrate similar behaviors? The temperature and number of sick students spike up and then go down in a relatively smooth curve.

It is clear that these two systems, which are completely different on the surface, share some similar underlying structure. It is useful to identify categories of systems so that we can apply what we learn about one to the other. By studying the math underlying the coffee cup temperature, we may gain a better understanding of flu progression and develop better prediction and prevention methods.

There are four major categories of systems, as shown in the table: deterministic, moderately stochastic, severely stochastic, and indeterminate. They are identified by the number and types of inputs and outputs.

A Deterministic System is where a change of input leads to one, and only one, output. The classic example of a deterministic system is a thermostat connected to a furnace. The input is a change in temperature. A change in input, i.e. a change in temperature, changes the output; the furnace turns on and heat is produced. If that does not happen, the system is broken; or if you get some other sort of output, say smoke, you know the system is broken.

Imagine for a moment that you had never seen a thermostat and you knew nothing about a furnace, but you thought they were somehow connected together in a system. What could you do to discover how the system works?

A Moderately Stochastic System that is somewhat unpredictable due to inclusion of one, or a very few, random variables where a given change of input leads to a quantitative change in output. The classic example of a moderately stochastic system is a casino. The inputs are the amounts wagered; the outputs are the amounts won. The important point here is that there is only one kind of output. The outputs vary in amount but not in kind. In a casino, it is often dollars for dollars, but for a farmer, it could be about hours spent preparing a field for bushels of corn per acre. In a football game, the only output that matters is points; nothing else counts.

These kinds of patterns can be studied using statistics. For instance, suppose you were interested in the chances of winning a bet, or the connections between hours-of-study and test scores. You may have a fifty percent chance of winning a bet, or the chances of passing a test with zero hours of study are about 10 percent but rise to 90 percent with 3 hours of study. These relationships can be explored with statistical methods that rely on a detailed understanding of the underlying system.

These two types of systems, deterministic and moderately stochastic, are the domain of laboratory science. These are systems that can be addressed with standardized protocols, controls, and observations. However, the next two kinds of systems do not lend themselves to that sort of approach.

A Severely Stochastic System has multiple random elements, where a given change of input leads to a limited range of different kinds of output. For instance, suppose you are in charge of a shoe factory. You wish to increase the profit so you decide to change the inputs by cutting everybody’s wages 10%. Do you increase the profit? Maybe, but there is a chance that you may also decrease productivity, or lose product quality, or increase sabotage, or have a strike. In short, a change in input has generated a possible change in the kinds of output. But the changes in the kind of output are limited. It is unlikely that anybody will bring you flowers.

So how do you think about, describe or analyze such a system? The short answer is you use logic. For example, you have to use equations in the form of, “If A is true, then B otherwise C; if it is sunny, we go to the beach, otherwise, we go to a museum. The same idea can be expressed more algebraically as IF X = Y THEN Z ELSE 0. To really understand this sort of system, these sorts of logic statements must be made for every interaction in the system. It does not take more than three or four elements in a system to outstrip our ability to keep track of what is happening. Beyond that, we need a computer’s help.

The last kind of system is Indeterminate: for a given change of input, an unknown and unpredictable kind of change in output occurs. These are systems with unknown, sometimes invisible, elements, some of which may be random, connected in unpredictable ways. The classic example is the evolution of a complex biological community. A more immediate example is climate change.

There are two ways of dealing with such a system. The informal approach is to use intuition. Intuition is our most powerful analytical tool when the system is complex, somewhat invisible, and somewhat unknown. We all know stories of how intuition saved the day in the face of incomplete and uncertain information. However, let’s be honest. Intuition is often wrong. How could it not be? It deals with incomplete data and information about the most complex systems we know.

When scientists are faced with an indeterminate system, they can use a more formal and effective process known as hypotheticodeduction. Reduced to the bare bones, this is a three-step process:

  1. You develop a hypothesis, “Maybe the system works or functions in such-and-such a manner or way.” In creating this hypothesis, you can use creativity, imagination, and any data, or information you can get.

  2. You then ask, “If the system works like this, what would I expect to find? What kind of information or data about an output would confirm my hypothesis?

  3. And then, you go out and look for that information or data. If you cannot find it, your hypothesis is unconfirmed. If you do, your hypothesis is supported.

Hypotheticodeduction is a very creative process. The development of a hypothesis is about brainstorming any and all possibilities and explanations. It’s sort of turning the world on its head to see what might happen. The only limits are set by the idea that the hypothesis has to be confirmed by the subsequent search for outcomes. You probably cannot hypothesize a system that produces rock-and-roll in the absence of guitars.

So, there are four different classes of systems of increasing complexity and uncertainty. Each class requires a different analytical approach of increasing complexity and uncertainty. If there is a mismatch between the analytical approach and the system class, there will be a waste of time and resources. Imagine using trial and error to determine how a factory functions or how your classmates perceive the benefits of schooling. But, recognize at the same time that simply saying you have a high probability of increased income if you stay in school does not paint a complete picture of the role of education in your life.

Part 5: Modeling Systems

The hypothesis that you develop about the structure and function of any system is a representation of some part of the world. It is a model. On a day-to-day basis, our hypothesis of how the world works is found in mental models. For instance, if a road is closed on your route to school, you have a mental model or map of an alternative route, an expectation of how late you’ll be, and what that might mean for the rest of your day. Or, you might have a model of the process to win a starting position on a varsity athletic team. Or, you can hypothesize what it might be like to double the students in your school.

Can you name or describe some of the mental models you have already developed or used today?

These are somewhat personal questions, but we can use the same sort of approach to answer more complex questions:

  • How do we know what medicine to give to someone who has cancer? Does it need to depend on their genetics or on what they eat, what they don’t eat, where they live, how old they are, whether or not they have allergies, or so many other factors?

  • Can we predict what happens if we reintroduce Grizzly Bears to the North Cascades?

  • Is it really worth the effort to dig wells to provide clean water to rural, poverty-level communities?

  • What will be the outcome of having the police sweep up the drug dealers in a city park?

The important point here is that even though you might use some of the more personal models frequently, you do not really examine the assumptions, connections, and ideas they contain. What you pay attention to is that they mostly work, and when they do not, maybe you can figure out why. Of course, a model of a complex system has to also be complex, with multiple connections and interactions. The assumptions, connections, and ideas they contain must be brought into the open and made explicit precisely because science is a public process.

This is the point where computers are beginning to play a very big role. The computer allows us to make explicit, complex models of systems that we just could not do before. We can now develop a hypothesis about how a system works, express that hypothesis as a computerized model, have the computer simulate how our model works, and generate an outcome or output. We can then compare that outcome with what we find in the world to support, or not, our hypothesis.

This is a hugely important revolution. We can now begin to look at the world in a different way - a more powerful, creative, and effective way. The computer allows us to deal with a greater degree of complexity than we could without their assistance. We can ask a whole new set of questions. We can ask about, and debate, a future based on shared, explicit, and comprehensible structures, information, and interactions. We can now deal with a whole range of really fascinating questions that were simply beyond our capacity in the not very distant past; for example, issues of climate change, or issues of terraforming Mars. Earlier it was said computers could change the way we think. This is where this change occurs.

But before we get started with building models, there is one more point that must be stressed. Every model, mental or computerized, that you have ever used, or will ever use, is incorrect. Let’s think about a physical model for a moment. Suppose you wished to build a model of a Boeing 747. The only way to build a correct model of the plane is to build the complete, functional, full-sized plane. But then it is not a model anymore; it’s a plane. The same idea holds true of mental and computerized models. They are always going to be less complex than the reality being modeled and are, therefore, incorrect.

We do not evaluate a model on its correctness, completeness, complexity, or difficulty to create. We say a model is good, or not good, based on its utility. Does it help us understand, predict, manage, or control what happens next? If it is does, it is a great model; if not, not so much.

Because every model is incorrect, there is always uncertainty both in the model itself and in the information and understanding derived from the model. The colloquial way of saying this is, “The map is not the country.” There is always the danger that we start thinking the model is more comfortable, or correct, or reliable than the reality and when we get divergence between the two, we trust the wrong one.

With that, we’re nearly ready to build some models.

Part 6: Building Models: Static or Dynamic?

This diagram shows a model of a cell phone network built using a tool called Cytoscape. This kind of representation is useful for mapping out the interactions, or edges, that exist between components, or nodes, of a network. This sort of model can be very useful for making a map of the basic structure of the system, and for making predictions about what might happen if the network of interactions were altered either by elimination or addition of an edge or node. This type of model is considered static because it only identifies whether interactions exist or not; it does not account for differences in strength of interactions or changes over time.

On the other hand, if you think about the systems you are familiar with such as the human body, the weather and seasons, or your school and classmates, it is clear that many systems are dynamic. They are constantly doing something; perhaps producing a product, growing, or developing and changing. Therefore, there are other kinds of questions we might want to ask about a system. For instance, how does a system change over time? Can a system grow? Can a system change its structure and activity? These are questions about the dynamics of the network, called its behavior over time.

In our daily lives, we ask and answer these kinds of questions all day long. Is school going to be different tomorrow? If I take the bus, how does that change my day? Should I say “hello” to that person or not? What difference will doing my homework tonight make tomorrow? These are the kinds of questions we spend a great deal of time on and are very interested in the answers.

In the context of scientific research, we are often interested in the dynamics of a system. If CO2 emissions are decreased, what will be the impact on the progress of climate change? If a species of fish suffers due to environmental conditions, what will happen to the predator populations? If a person receives an experimental drug, how does their disease respond over time? If a whole population of patients receives an experimental drug, does it help more of them than not?

We are therefore very interested in modeling complex dynamic systems. To do this, we will need to use tools that allow us to create systems using stocks instead of nodes and flows instead of edges. Stocks are quantities that can be measured, such as fish population, temperature, or number of sick patients. Flows are processes that influence the stocks in some way - for example, predators feeding on fish, or drugs being given to patients. This type of system is far more quantitative than a static system. The influence of one element on another can be quantified with numbers or mathematical relationships.

An example of a rich dynamic system is illustrated below. This model was built with Stella Online, a program you will use as part of this module to model population dynamics. Click on the image to see the original model and interact with it. There are many modeling programs available, including NetLogo, Vensim, Sysdea, InsightMaker and many more.

This Stella model of a city's traffic congestion represents a dynamic system in which the stocks are Roads, Roads Under Construction, and Population (rectangular icons). The large blue arrows with handles represent flows directly changing the quantities of the stocks. The circles are converters which influence the rate of change of the elements they are connected to. The arrows are links demonstrating relationships between elements of the network. Take a moment and “read” this model and try to link it with your prior knowledge. What factors are influencing the amount of traffic congestion in this system? Can you identify any positive or negative feedback loops? For example, if the number of roads increases, the number of roads available increases, which reduces congestion - negative feedback. A more complex example loops through the whole system: if population increases, congestion increases, creating pressure to expand roads, which eventually leads to road construction, increase in roads available, and once again congestion drops - a longer process of negative feedback, bringing congestion back to acceptable levels.

If we “run” this model, which means allowing all of the elements to progress through a “simulation” of a certain amount of time (anywhere from nanoseconds to years and beyond, depending on the situation), Stella produces a graph of the system’s predicted behavior over time (a behavior over time graph, or BOTG). The graph represents two key elements of the model - the number of roads (red), and the amount of congestion (blue). What do you notice about the shapes of these two graphs? Do they seem realistic? Often, a BOTG can provide important clues about the accuracy of your model.

Part 7: All Dynamic Systems Show Behavior Over Time

An important reason for using a systems approach when thinking about problems is that systems behave in very consistent ways. What you learn about one system can often be directly applied to another, so long as the internal system structures are similar. Think of the universal concepts of negative and positive feedback loops that appear in almost all systems. There are many common underlying structures built from these loops that result in similar BOTG structures. System scientists have distilled system behavior down to just a few fundamental types.

Linear growth and decline are behaviors with which we are all familiar. They are very predictable and not often seen in real life systems over long periods of time.

Exponential growth is common in systems. Sometimes exponential growth it is perceived as being linear because the time frame that we consider is very short. In the graph to the left, if you only consider data between 10 and 20 months it appears very linear.

There are limits to everything and for that reason growth toward a limit is commonly found in systems. Just about anything you can think of requires resources, and resources are never unlimited.

Although the universe is filled with examples of growth, everything eventually goes into a period of decline. Sometimes decline or decay is linear, but more often the rate of decline changes as time goes on, leading to what is called exponential decay.

Some of the behavior seen in systems is a bit more complex, showing evidence of combinations of more simple behaviors. S-shaped or logistic growth is exponential at first, but at some point transitions into growth toward a limit.

Oscillations are the final fundamental behavior we will consider in systems. They too are complex, but often fluctuate around some more simple behavior pattern. The oscillation seen here looks like it might be fluctuating around a stable linear pattern or perhaps growth toward a limit.

Consider the traffic congestion model again. Which of these six patterns do you observe? The number of roads seems to increase in a linear fashion, though it’s possible it would be exponential growth over a long time scale. On the other hand, the congestion amount is clearly oscillating up and down. This occurs as the balancing feedback loops do their work over time. Population growth increases congestion, but responsive road building brings congestion back down, and the cycle repeats.

These six basic patterns make up most of the behaviors that we can observe and directly relate to something other than randomness in systems. Randomness certainly does arise in our experience of the world, and humans have developed ways to model the chaotic or stochastic behavior that arises from it, but these techniques will not be addressed in this module. Regardless, there is much to be learned about the world and how things work using the tools of system dynamics.

Thinking about time

System dynamics models are concerned with behavior over spans of time, but how much time is appropriate? The time dimension is extremely important in any model, whether it be mental or mathematical. Some units and spans of time make absolutely no sense when held up to some models. Would you, for example, ever consider the problem of the extinction of the dinosaurs using a time unit of seconds? Or look at your life-span in millennia? Of course not. The units of time that you choose for your model are important and should be appropriate in scale. In the traffic congestion model, the simulation was run over a period of years, an appropriate dimension for the situation.

The time span of the model is also important to think about and should be chosen as a function of the problem you have defined. The rule of thumb is that the time span should be long enough to include all of the expected changes in behavior, but not so long that there is a chance that any change in dynamics could be caused by some new parameter or connection not currently included in the model. The graph for the traffic congestion model spans 50 years. It would be important to think about whether the elements of the model (for example, the rate of population growth) would remain steady over such a long time span. If not, perhaps it is more accurate to look at a shorter time span.

Activity: Consider each scenario. What time unit and time scale would you choose and why?

  1. Snowpack in the Cascades

  2. Changing velocity of a skydiver

  3. Time to process data in a computer chip

  4. Geological history of the Pacific Northwest

  5. Global climate change

  6. Photosynthesis in an algae cell

Let's Get Started!

Now that you understand the fundamentals of systems and models, you are ready to dive into creating models yourself! This site consists of several activities of varying complexity. Each guides you through using a tool to create a specific model. Through this work you will gain an understanding of how a messy, real life system gets turned into a manageable model. When you are ready, you can tackle the "Create Your Own Model" exercise, and if you want, share the models you make with us. We can't wait to see what you come up with!


Dexter Chapin: Teacher Scholar, Seattle Academy of Arts and Sciences

Anne Gilles: Teacher Scholar, 2019, ISB

Steve Roderick: Teacher, Scholar 2015, ISB

Kauffman Jr., Draper L. (1980). "Systems 1: An Introduction to Systems Thinking." The Innovative Learning Series. Future Systems, Inc.

Funding to support the development of these activities and experiences was provided by the National Science Foundation Award DBI-1565166 & 0640950. The content of these pages was created by students for students with the help of teachers and scientists. The views expressed herein are those of the authors and do not necessarily reflect the views of NSF or ISB.