 So, brief introduction I want to give today is on something called as patterns of behavior which is kind of follow-ups on that. See, we all, why we are trying to do system dynamics is because the behavior of system arises from its structure. It is fundamental idea that we are trying it out. We are not saying that the entire behavior of system is exogenous. If you do it, then there is nothing, there is no need for solving any issues or trying to model a system. We are trying to understand only because we know that the behavior under system arises from its structure. So, in this set of lectures, what we are going to do is overview the dynamics, what kind of dynamics actually are out there, how many types of graphs we can actually see. And based on that, is it possible to actually isolate or classify these dynamics? And if we can think of classification, surely people have already worked it out. And are there any generic structures that we can come up with in our causal diagrams that we have been seeing which can be used to kind of explain those dynamics. So, that is what we are going to see without much funfair. These are the basic modes of behavior. Exponential growth, goal seeking, S shaped, oscillations, growth with overshoot, overshoot and collapse. Of its exponential growth, it is very easy to imagine and goal seeking and oscillations are kind of very fundamental behaviors. A combination of these three systems is what results in other behaviors called as S shaped growth, growth with overshoot and overshoot with collapse. So, this goal seeking can also have a behavior from zero and saturating there that is also kind of goal seeking, you can go like this. Exponential is increasing like this, so other one is called as accelerated collapse which goes like this and then falls down like that, so that is called as accelerated collapse, which is common in when stock market collapses it is usually not a slow collapse, it is an accelerated collapse almost overnight things crash, then that can be modeled as a using the same underlying structure that we used to model exponential growth. Let us quickly look at it, exponential growth that means, there is a positive self reinforcing feedback in the system that means, the system is there and the net increase, there is a net increase in the system and that contributes to the system, again contributes to the net increase rate and that is going to feed each other until it causes an exponential growth. So, a simple example could be if you have a bank account then interest keeps adding to the account and then every year it gets gets kind of accumulates, though the amount may be small we leave it for 100 years then you get a really large amount of money, so that is the exponential growth. So, state of system if you plot you will get a exponential increase, it is common in many scenarios for example, if you are modeling the what is it US GDP, the average growth rate is 3.45 percent per year and doubling time is 20 years, US prison population again as I told if you draw the correlation it will be high, but that does not mean anything. So, or world population transistors per chip or many other behaviors of biological systems wherever you may see in paper you may see many such graphs for a system, so all it means is there is an underlying positive feedback reinforcing loop where the net change in loop affects the state of system which affects the net increase rate in a positive passion which results in exponential growth. So, if you see such behavior that is underlying model that we have to discussing where is that loop that is occurring. Positive feedback need not always generate growth, it can also create self-enforcing, reinforcing decline that is it will accelerate a decay like a drop in stock price erodes investor confidence which leads to more selling lowest prices still lowest confidence, but it happens so fast that it results in collapse. Many such thing in India you can have heard like you know when I am not sure whether you have heard it like this chip funds and when there is a rumor that bank or wherever you have put money is unable to pay you then there is huge rush of people suddenly trying to withdraw money leading to a collapse that is what I mean by accelerated collapse. Initially people are fine then suddenly one guy goes and he is generate money today then he goes and talks to people and then suddenly the message goes so fast that it results in accelerated collapse in the system. What about linear growth? Linear growth is actually quite rare. Linear growth requires there is no feedback from the state of system at all it just happens on its own there is no feedback because net increase rate must remain constant even of system state changes only then you will get a linear growth we just plotted it. So, that means there is no feedback coming in about state of system. So, then there is so what so the other one is what appears to be linear can actually be exponential, but viewed on a very short horizon. So, time horizon is very very small you will find that the growth looks linear, but actually if you wait long enough it will result in a feedback within the system. So, that is the exponential growth. So, general structure for a goal seeking behavior that is the graph we saw. So, whenever there is a goal that seeking behavior it means there has to be a goal that is entered you know the title is self revealing there is a goal that is a goal seeking there is a desired state of system there is actual state and based on discrepancy I am taking into a corrective action correct and I am going to correct it until I reach the goal whatever it is. So, this negative feedback loop acts to bring the state of system in line with the goal or the desired state that we want it is quite intuitive the behavior we can expect it something like this. The goal can be approached from the bottom to the top or from top to the bottom. There are nice examples like semiconductor fabrication defect rate to model defect rate it is exponential kind of goes down exponentially that is goal seeking behavior, nuclear plant load factor can rapidly increase up to about 80 percent load, but after that it is very very slowly it increases or television share of all advertising US traffic fatalities per vehicle. So, all these things show a kind of a goal seeking behavior over time. Again x axis is time looking at time changing behavior. The third fundamental mode is called oscillations like goal seeking behavior oscillations also caused by negative feedback loops, but something is constantly changing that is what oscillations mean. This is very simple modeling kind of construct that causes that fluctuations is the presence of delays in the system. If you do not know the current state precisely then you are going to assume something and take a corrective action and the corrective action takes some time before it affects the state of system and it takes time for you to observe the state of the system and then identify the gaps and then decide which corrective action take. So, all these delays allow makes us to overshoot our goal then again go below the goal then again we take corrective action go above the goal etcetera. So, you are kind of oscillating throughout or oscillating over time. So, overshoot arises from presence of significant time delays negatively. So, when you observe systems whose graphs has oscillating behavior then the thing you should understand is there are some significant time delays being involved. Let us start to identify those time delays what is causing the delay how we can reduce it or just identifying it right now we are not prescribing action we are only trying to understand and discover what is happening. So, if there is oscillations for example, it takes time for a company to measure report inventory level trust me or not people do not have good inventory visibility. If you look at a warehouse it takes a week or even a month to figure out what is the inventory, but during the month there are so many transactions. So, value you got was itself kind of redundant now. The time for management then has to meet based on that in all managers will meet have some meeting two three weeks later make some nice fancy PowerPoint presentations and somebody will say this is a corrective action and then some memos will be issued and corrective action or suggestions will be taken. So, all these things involve lot of delays. The result is you are going to have oscillations right sufficiently long delay to any one of these points will cause inventory to oscillate. So, the underlying structure is very similar to goal seeking system except that now there is a measurement reporting and perception delays in a system between a state and discrepancy. Discrepancy to corrective action there is administrative and decision making delays that is involved in the system and between corrective action to state of system there are something called as action delays. Even if I say this is what has to happen we do not do it. Even if you know assignment is due tomorrow yes I have to work on it he will say she care which I pick idea. So, that is called action delay. There is delay to your action and then it will ask you to oscillate and again we are not trying to solve the problem we are just trying to understand and model it right now. So, again unfortunately this is a nice graph unfortunately reality is not so nice and smooth, but still you can figure out there is some oscillations that is happening like capacity utilization manufacturing or unemployment rate or US real GDP. So, that means, there is a lot of delays that is happening without decision making it is not that people do not have goals people have goals, but somehow there is lot of delays at various points let us try to uncover that and capture it in our model. So, that is what this tries to teach us. So, these are the fundamental modes exponential growth positive loop goal seeking negative feedback loop or there is a goal oscillations there is a negative loop with delays. A mix of these can can cater to more variety of behavior more complex patterns which are where there is a non-linear interaction in the structure. So, exponential growth and goal seeking will find that the underlying structure is actually linear model. So, you can actually apply various linear control systems techniques to look at that, but one system becomes non-linear when we get more interesting behaviors you can get S shape growth, S shape growth, overshoot, overshoot collapse and things like that. Let us quickly explain what is S shape growth. No real quantity can grow forever eventually one or more constant holds the growth. A commonly observed mode of behavior in dynamic system called S shape growth. That is growth is exponential at first and then gradually slows down until I hit the state-out system. Rapidly increase and then slowly saturate or reach the equilibrium. It kind of resembles a stretched out S. So, one way to understand it is there is some sort of a carrying capacity in the system. Take or rather initially the system is allows you exponential growth after which some constraints starts limiting its growth. Recall the land use example I talked about. Currently there is lot of lands of people started coming and as the lands capacity starts increasing we can expect that the growth will cease at some point. So, that is what is written here. So, S shape kind of a stretched out S. So, the first part you can see here is exponential increase at some point it starts to slowly saturate. Initially the positive feedback is active and starts growing the system very nicely up to this point after which the carrying capacity of system that how much system can observe will start to dominate and then it will decrease overall rate of increase which will allow system to saturate at some point. You can see many such examples like say growth of sunflowers, US cable television subscribers, adoption of pacemakers by physicians. When will UK hit smartphone saturation? So, many such options are given all other kind of S shape saturating. So, once everybody buys cell phones they are saturated. Now, you are expanding people second cell phone, third cell phone etcetera. They are looking at replacement purchases and things like that. So, there is a positive loop with a negative loop again there is no major delays in the system without delays itself it kind of shows this shape over time. If a delay happens what will happen? We can expect some oscillations right this exactly will happen. If there is significant time delays in the negative loops then you end up having oscillation because you will overshoot your goals and then again you have to take a very drastic active action again it falls down. Very similar idea exponential growth again over goal, but there was a delays before negative feedback kicked in. So, it allowed you to overshoot and then again you take more corrective action came down and again you go up and kind of fluctuates. So, whenever graph goes up and then kind of comes down maybe it is going to go again up sometime in future. So, exponential growth kind of tipping and coming down or similar here aluminum production goes up saturates and then starts fluctuating at around a point perhaps it is an S shaped growth. So, here there is no rules no regulation lot of aluminum production zoomed after that you are starting using the resources that puts a constraint in the system. Second critical assumption underlying this S shaped is that carrying capacities is fixed. If some reason the carrying capacity starts eroding faster you are not going to oscillate you are going to come down crashing because system cannot take it anymore. So, that part is for example, population of deer can grow so large that they over browse vegetation leading to starvation and precipitous decline in the entire population itself. So, behavior could be it increases and then goes above your capacity it starts oscillate, but then rapid collapse happens. So, the left half is same as what we saw earlier a few minutes ago, but now the carrying capacity also is affected by state of system consumption erosion of capacity. So, as capacity falls down this loop becomes more tighter that means you actually reduce your goal a nice ambition, but whatever reason your goal itself eroded. So, once the goal eroded then your entire system state will start following that particular goal because this becomes a dominant loop. So, why care about these behavior modes? See the principle that the structure of system generates behavior is very useful heuristic. So, we can try to learn to ask right questions it helps modeler discover the feedback structure of system. When we see data and patterns of behavior we can then know what basic feedback structure might have been dominant different points in time. If you see a shape then you know there was some positive feedback sometime in the past. So, what was it that was enabling it? Maybe it was a good administrator, maybe there was absence of rules something else happened upgrade, but now it is not it is kind of saturating. So, is there any other dominant loop that is happening? It allows us to uncover what kind of dynamics that could have occurred which we will get only if we look at it over time. So, it is not. So, math alone is not going to help you just getting your correlations and it is not going to help you have to understand what might have increased then what kind of links could have been there and then work with that. Quick caution is if you are only looking at the past then we do not know what is happening in the future. So, that also has to be kept in mind. So, I want to give this quick introduction because we will be revisiting this again and again or I expect you to revisit it again and again because in this course what we are going to do is from next class say model the positive feedback system, simulate it, learn how to actually put in numbers and simulate see the properties how it were happens then simulate goal seeking systems various kinds of goal seeking systems whether they are able to achieve the goal not achieve the goal things like that and then we will start introducing delays within them and see we are able to replicate these kind of behaviors. So, when as suddenly go doing that and then we will do a shape growth we will do more complex systems where you know in mix of all these behaviors. So, it will be good for you to always come back to this and use it as a reference ok because sometimes the model becomes so complex because using so many variable but underlying structure will be only this we added more variables just for the completion of problem but the core structure will always come back to this. So, you keep this as a reference keep looking at it but we will be spending enough time with each types of behaviors in the first half of the course and second half we will start looking at modeling of system more deeper analysis and more prescriptions and things like that. Thank you I will just stop here.