
Modelprojekt, 1. modul, 2014, id:468  
Vejleder:  
Findes på RUb:  Ja 
English abstract
The main focus of this article is to observe and describe how a population will change in time as a function determined by another population. More accurately there has been constructed a simple and a modified dynamical system used to describe the change in the number of users on facebook on both PC and Mac as a function of time. The simple model (formel) simply says that either you already have facebook  or you do not. If you do not, you are in a population where everyone without facebook has the same probability of creating an account on facebook  the only difference is whether you own a PC or a Maccomputer. If you already have facebookaccount, you have the same probability of deleting your account as the other users on your given system. This results in a state of equilibrium. When analyzing the parameters it became obvious that the rate of people deleting facebook will determine the number of constant users, while the rate of people signing up will determine how fast you reach the equilibrium. The modified model (formel) is essentially the same. It, however, has one small factor changed: Once you have deleted your facebook account, you will not be interested in signing up again. This small change alters the entire result as there no longer will be a state of equilibrium. The amount of facebook users will climb to a global maximum before declining slowly  but steadily. There will still be new people creating accounts, but it cannot match the amount of profiles being deleted. It has been impossible to get accurate parameters  which is why they have been determined as good as was possible. This, however, means that the graphs and predictions might not be accurate, but they should still give a good indication of how the amount of facebook users should climb and fall as time goes by. Essentially facebook will eventually lose popularity if this model has a shed of truth in its prediction. The only question remaining is how long facebook can remain the monarch of social media and who will eventually take over.