 Up until now, our model of a system has been relatively static. In this module, we are going to start to deal with how systems change over time, what is called System Dynamics. System Dynamics is a branch of systems theory that tries to model and understand the dynamic behavior of complex systems. It deals with internal feedback loops and time delays that affect the behavior of the entire system. It was first developed by Professor Jay Forrester at MIT as a management method but has since gone on to be applied to all types of systems from modeling the dynamics of Earth's systems to those of the economy and political regimes. The key elements of System Dynamics are feedback loops, stocks, and flows. Firstly, feedback. With analytical thinking, we often see the world in terms of linear cause and effect, but systems thinking looks for the interplay between elements, that is the feedback loops through which elements are interconnected in affecting a joint outcome. System Dynamics uses what are called causal loop diagrams to do this. A causal loop diagram is a simple map of a system with all its constituent components and their interactions. By capturing interactions and consequently the feedback loops, a causal loop diagram reveals the structure of a system. By understanding not only the structure to these relations, but also the nature of those relations, it becomes possible to model and simulate a system's behavior over a certain time period. These feedback loops can then be of two different kinds, either positive or negative. A positive feedback loop means that values associated with the two nodes within the relation change in the same direction. So if the node in which the loop starts decreases, the value associated with the other node also decreases. Similarly, if the node in which the loop starts increases, the other node increases also. Economics of scale is an example of a positive feedback loop between a business and its customers. The more products a company sells, the more revenue it receives from its customers, giving it more to invest in scaling up production, thus allowing it to reduce costs, which in turn means more customers will purchase the product, and so on. This is also called a virtuous cycle, where one party gains, the other does so also. Of course, this can't go on forever, and that is why positive feedback loops are typically associated with unstable processes that are likely to crash at some time. A negative causal link means that two nodes change in opposite directions. If the node in which the link starts increases, then the other node decreases, and vice versa. The systems dynamics between predators and prey are an example of a negative feedback loop. If the number of predators increases, then the number of their prey will decrease, which will in turn feed back to affect the predators by reducing their population, which again will feed back to increase the prey population, and so on. Negative feedback loops are typically associated with an overall stable and sustainable pattern of development. There are, of course, many more examples of positive and negative feedback loops, but we will move on to talk about the other key feature to the area of systems dynamics, that is what we call stock and flow diagrams. To perform a more detailed quantitative analysis, a causal loop diagram is transformed to a stock and flow diagram, which helps in studying and analyzing the system in a quantitative way, typically through the use of computer simulations. A stock is the term for any entity that accumulates or depletes over time. Thus, it is a simple variable. A flow, in contrary, is the rate of change in a stock. So an example of a stock might be a water reservoir. It is a store of water, and we can ascribe a value to the volume it contains. Now, if we put a tap on the side of our reservoir and started pouring water out of it, this would be an example of a flow. Whereas a stock variable is a measure of some static quantity, a flow variable is measured over an interval of time. By using these tools of system dynamics, we may get a qualitative and or quantitative idea of how a system of interest is likely to develop over time. For example, if we create a simple two-dimensional graph with time on the horizontal axis, we will see how the different feedback loops create different types of graphs. Graphs for positive feedback loops typically reveal an initial exponential growth as they shoot upwards rapidly, then reach some environmental boundary condition where they crash back down again. A financial bubble and ensuing crash could be an example of this. Whereas the net result of a negative feedback loop will be a wave-like graph that will likely be bounded within an upper and lower limit over a prolonged period of time with relatively smooth fluctuations during the system's development that enable it to sustain an overall stable state in the long term.