Engineering System dynamics is a modeling method for the analysis of complex engineered systems that are characterized by feedback loops and time delays. It is a holistic approach in that it gives us a view of the primary interactions and their feedback effects that drive the functioning of the entire system. It is used in many areas from trying to model ecosystems to economies and large engineering projects.
Linear Cause & Effect
In simple linear systems, cause and effect interactions happen through a unidirectional process. Cause A creates an effect B, we hit a ball with a bat and the ball moves off in the direction we hit it. We buy a product, use it and throw it away. These are linear processes involving cause and effect interactions that are characteristic of simple systems that have a low level of interdependency. We typically tend to think of things as chains of cause and effect and often ignore the time delays between them, and how a change in one component will possibly feed back to affect its source. This linear cause and effect paradigm is part of the analytical method of reasoning that focuses on the individual components in a system and uses linear equations to describe how they interact in a well-defined manner.
Nonlinear Cause & Effect
But in complex systems where the components are highly interconnected and interdependent, cause and effect interactions are no longer one-way, but in fact, feedback on each other. In these highly interconnected systems, a change in one component will not only affect another, or possibly several others but how it affects the other components will in turn feed back to affect its future state. The big idea here is that of interdependence, which is a key characteristic of complex systems. Because of heightened connectivity, everything affects everything else and this effect doesn’t just disappear. Sooner or later it feeds back to its source. We cannot just put large amounts of CO2 into the atmosphere and expect it to disappear. It will sooner or later feedback to affect the source, and it is these macro-scale feedback loops that really govern the system’s overall development in the long term. This is in the long term because in the short term the system’s environment may be large enough to absorb and retain this effect without it feeding back to its source. After all, our industrial economies managed to put a lot of CO2 into the atmosphere before this effect started to really feed back and affect the economy itself, but in the end, it has. Thus, we use the term time delay to refer to the fact that it may take time for these effects to feedback to their source.
Causal Loop Diagrams
System dynamics recognize relations of interdependency and provides us with models to focus on these two-way interactions, through what are called causal loop diagrams. Causal loop diagrams or CLD’s are maps that model the set of relations within a system. They try to capture how the change in a variable associated with one component in the system will affect another, and these causal relations are called causal links. When causal links between related variables feedback on each other, we have what is called a feedback loop. With feedback loops, we are asking how the relation between two variables affect each other, and there are really just two types of feedback loops, positive and negative feedback.
A positive causal link is one where the variables associated with two components move in the same direction. So if one goes up the other goes up also. If it goes down the other does likewise. A positive feedback loop is when an increase in one variable affects another in the same direction, but this change then also feeds back to change the source variable in the same direction, and thus it is a self-reinforcing loop. For example, the relationship between honeybees and flowing plants is a positive feedback loop. The more bees we have the more plants we can have, and the more plants we get the more bees that can be supported. In other words, more begets more. Such feedback loops generate exponentially escalating behavior, which can be very beneficial or very detrimental. Traffic jams are another example of positive feedback loops. The more cars that join the traffic jam the slower it will move. The slower it moves the more cars that will join. More begets more.
Virtuous & Vicious Cycles
This example of traffic gridlock is called a vicious cycle because with each iteration of the cycle it reinforces the previous one, continuing the cycle in the direction of its momentum until an external factor intervenes and breaks the cycle. Hyperinflation is another good example of a vicious cycle. Through positive feedback, the value of the currency stays spiraling down. Investment in infrastructure might be an example of a virtuous cycle. The more we invest in infrastructure the more efficient our economy may become in the future, meaning we can retain more public revenue for reinvesting in infrastructure and the cycle begins again. But of course it can’t go on forever and that is why positive feedback loops are typically seen to be unsustainable. We might think of urbanization as a positive feedback loop. The more people that move into urban centers the more resources are concentrated in them, allowing them to leverage economies of scale to be more economy efficient. But also it has a negative externality in that it reduces the rural population, and thus the capacity to provide desired services in the countryside. Both of these, the positive feedback and negative externality, work to attract more people into the city. But again this creates an unsustainable dynamic and we end up with the overpopulated and underserviced megacities like Jakarta and Lagos.
Negative feedback loops are relations where the variables associated with two components feedback to affect each other in the opposite direction – the more of one, the less of another. The more fishing we do the less fish there will be, which will feed back to reduce our capacity to fish during the next season. This is also called a balancing loop. Thermostats use negative feedback to balance the temperature of your house, as do all forms of control systems. In order to maintain the state of the system, they are regulating around some optimal equilibrium state. The ballcock or float is another example of a control system that uses negative feedback to control the water level in a reservoir. When the water goes up the float cuts in to reduce the inflow and vice versa, creating equilibrium within some set of parameters to the water level.
Positive & Negative Feedback
Within complex systems, these causal loops do not exist in isolation, but there are in fact many different positive and negative feedback loops and links interacting. And thus, we need to draw a whole map of these different causal interactions and loops in order to understand the system’s overall dynamics. Real world complex systems are typically held in their current configuration or manifest a certain behavior because they are under many both positive and negative feedback loops, with the strength of these different loops changing over time to create some dynamic state.
System dynamics models capture aggregate variables. As such, they give us general models of behavior and trajectory, answering such questions as to what is the general shape of the graph generated by the system over time? Will it be oscillatory, as negative feedback dominates or will we get nonlinear exponential growth and collapse when positive feedback dominates? As such, outcomes to these models should not be interpreted as predictions but more as general overviews, and this is often the best we can hope for when dealing with these very complex engineered systems. They help us to reason about what underlying structures need to be changed in order to change the system’s actual mode of behavior.
This is classical systems thinking and it can be of great value because our traditional more analytical modeling methods are often very brittle, meaning because they are based on very quantitative methods they are either exactly correct or they give us figures that blind us to the overall trajectory. The classical example of this being macroeconomic analysis which is based upon linear models, which may be exactly correct when it tells us that the Chinese economy will grow by 6.8 percent next year, but also completely fails to predict massive nonlinear changes brought about by financial crises. The nonlinear models of system dynamics help us from being blinded by over-analytical methods and help to predict these nonlinear changes that are driven by positive feedback. These nonlinear dynamics are behind many important phenomena within complex engineered systems such as disruptive innovation, the emergence of industry standards, lock-in effects and economies of scale within manufacturing.
System dynamics models help us to try and focus on the real drivers of change and sources of problems. They also let engineers and policy makers experiment with simulations in order to try and model what effect some intervention in the system will have on other variables and the whole dynamic. They have been used for everything from modeling the working of the energy sector, to the development of innovation and environmental policy making, to the modeling of urban dynamics and critical infrastructure protection. Systems dynamics was used as the modeling framework for the limits to growth publication, where researchers looked at how the variables of population, industrialization, pollution, food production and resource depletion interacted to create the long- term trajectory of the global economy and a possible limit to its growth.
Researchers at Delft University in the Netherlands use system dynamics models to try to understand and simulate the behavior of Europe’s electrical power grid, as different actors such as household consumers, power generators and policy makers all with different agendas interact to define the state of the system. By understanding the different motives that the different actors are under and the causal links within the system, it is possible to start creating computer simulations and alter certain parameters in order to see what happens. We might change government subsidies to see how this will affect the price producers set per kilowatt hour, and what effect that will have on consumer demand and how this might feed back to affect the producer’s price again.
Most of all causal loop diagrams help us to understand self-organization. As we saw in the previous module, complex engineered systems are distributed systems without centralized control. Patterns of order emerge through the process of self-organization, and feedback loops are key to the dynamics of this process. Without nonlinear interactions and feedback loops, self-organization doesn’t really happen. For example, negative feedback is a self-organizing mechanism for load balancing. If we think about toll booths on a highway, the system has a certain load, and as new cars approach they navigate towards the booth with the least load. Because of negative feedback, the more cars there are at a particular booth the less likely a new car will be to enter that lane and vice versa. There is no one coordinating this process. The load balance is an emergent phenomenon of self-organization through negative feedback, and it works to balance and stabilize the system.
The network effect that is behind the rapid adoption of many new media technologies like Facebook and Twitter is an example of self-organization through positive feedback loops. The network effect describes how the value of a technology or system is dependent upon the number of users of that technology, the telephone being a classical example. Without any users, it has no value, and every time a new person joins the network this adds some value to the technology for all other users. The more people that join the network the more attractive it becomes to the next prospective user. A new technology that can leverage this positive feedback loop can develop very rapidly to become a default solution and this is one reason why the networked technologies of I.T. are highly disruptive and can scale at an unprecedented rate. A thing to note here is that the value of the technology is really in the network of connections, not so much the technology itself. Facebook may not be the best social network in terms of design but everyone joins it because of the wealth of the network.
Lastly, complex engineered systems like cities, logistic networks, and the Internet are nonlinear, and nonlinear systems are deeply counter-intuitive. They exhibit many phenomena such as the butterfly effect, emergence, long tail distributions and so on, all of which means they can produce radical disruptive events, what are called black swans, which are statistically virtually impossible within linear systems but do occur in nonlinear systems. We are programmed to think in a linear fashion. As soon as we identify some stable pattern, we believe we can predict the future by taking this and projecting it onto the future in an incremental fashion, and for linear systems, this is often possible. But in complex systems with all of these nonlinear interactions, iteration, and feedback, they don’t develop in an incremental fashion. But these periods of transient incremental progress and stability are punctuated by rapid seismic shifts, what are called phase transitions, on the other side of which the system is very different. Because of these phase transitions the future emerges and it is often very difficult to predict with any accuracy, and chaos theory has taught us that there is a deep uncertainty to the development of nonlinear systems.
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