 class started today. Today we are going to look at a new topic on the dynamics of negative feedback system and through that I will introduce you to hands-on modeling using Vensim software. Before we get to Vensim, let us take a look at what is this negative feedback system. We have seen the negative feedback is characterized by goal directed or goal oriented behavior. Common similar terminologies include self-regulating or adaptive terminologies we end up using most of the control systems models where there is feedback involved falls under this category where you are looking at current state versus an actual desired state and then start taking the gap between them and try to control the system. So, most of the systems are going to study there is also can be task-fied as a negative feedback system. Examples is room temperature control or blood sugar regulation things like that. So, CLD representation of that would be a this is a kind of example base where we are looking at current state of the system. So, this is actual room temperature represents a current state we need we know desired room temperature we fix it in the AC all the time because the difference in according heating or cooling whatever it is has to happen. We know that the state of system can be represented as a stock, desired behavior is defined as a goal of system and discrepancy is used to affect the rate which then in turn affects the stock of the system or the state. This is a general causal diagram of a simple negative feedback system. This goal directed action is fundamental to any human social systems also always there is some sort of a goal towards which we are working on in this current state and we look at the gaps and the gap is too high then we start talking about inequalities and things like that or access to basic services and needs and try to come up with some policies or actions which will fulfill that gap. Let us look at the general stock flow diagram of this negative feedback system or a balancing or goal seeking system or a balancing loop system. So, you can simply represent state of system as a rectangle and this net inflow rate which flows into the stock and changes the stock we have desired state of system let us denote as s star we take the discrepancy and we adjust that discrepancy some fraction f every time unit until the desired state is achieved. So, this is a very general structure of the system. So, let us goal seeking or negative feedback systems as we just saw we have a stock s which is affected by some net inflow rate I have desired s star I have a gap we are taking the gap as s star minus s you can simply denote fraction per time denote by some f as shown here. So, we already know that net inflow rate or net flow rate d s by d t this is your net inflow rate as given in this diagram which is nothing but f into s star minus s this is this f represents the fraction of discrepancy kind of added per time. There is a gap and some fraction is what we are fulfilling every time unit or it is also called as a fractional adjustment. In most of our time it is not possible to completely eliminate the gap at one time step itself it takes some time for the room to cool down. Every time some small amount of this difference is kind of added if you think of stock as a current room temperature and the desired cooling that we want. So, some small amount of gap is kind of satisfied every time unit. So, that is what we are modeling here and the rate at which it is going to happen is defined by that fraction. So, fraction of discrepancy added per time or the fractional adjustment rate is what is defined as f. We can also denote say A t which is nothing but the adjustment time which can be defined as just 1 over f. So, if we are instead of fractions if it is time is more convenient to us we can define adjustment time which is just 1 over f and we can rewrite the original equations as inflow as d s by d t C s star minus s divided by A t, A t is the kind of a symbol for adjustment time. So, in coming up with a model for this negative feedback system all we need to define is the stock, desired stock and immediately we know the gap and the equation for gap is nothing but desired minus the stock. And so inflow rate we are all we are going to do is either multiply by a fraction rate per time which is f or we are going to divide by adjustment time which is very equivalent and we define our net inflow rate. This is what we are going to learn to model today. Before we start modeling let us start with kind of a three very basic pointers. When you build stock flow diagram base simulation model, stock flow simulation model, SD model as we call it always remember model should run without error all units in model should be ok and model should start in dynamic equilibrium. What I mean by dynamic equilibrium is for the given values in the system at the start itself we do not need to observe any dynamics in the system it should remain kind of constant. We will look at it through an example and when some suppose these features where you can check whether there is any units are all ok and debug the models if it was an error just check where the error is and then fix it. We will learn all these points through a simple example.