Introduction to the Modeling and Analysis of Complex Systems

44 CHAPTER 4. DISCRETE-TIME MODELS I: MODELINGRun this code and you should get a new window that looks like Fig. 4.1. If not, check yourcode carefully and correct any mistakes. Once you get a successfully visualized plot,you can clearly see an exponential growth process in it. Indeed, Eq. (4.12) is a typicalmathematical model of exponential growth or exponential decay. You can obtain severaldistinct behaviors by varying the value of a.1816141210864200 5 10 15 20 25 30Figure 4.1: Visual output of Code 4.9.Exercise 4.5 Conduct simulations of this model for various values of parametera to see what kind of behaviors are possible in this model and how the value of adetermines the resulting behavior.For your information, there are a number of options you can specify in the plot function,such as adding a title, labeling axes, changing color, changing plot ranges, etc. Also,you can manipulate the result of the plotting interactively by using the icons located at thebottom of the plot window. Check out matplotlib’s website (http://matplotlib.org/) tolearn more about those additional features yourself.In the visualization above, the horizontal axis is automatically filled in by integers startingwith 0. But if you want to give your own time values (e.g., at intervals of 0.1), you can