Introduction to the Modeling and Analysis of Complex Systems

42 CHAPTER 4. DISCRETE-TIME MODELS I: MODELINGyour Python and make sure you don’t get any errors. If so, congratulations! You have justcompleted the first computer simulation of a dynamical system.Of course, this code doesn’t produce any output, so you can’t be sure if the simulationran correctly or not. An easy way to see the result is to add the following line to the endof the code:Code 4.5:print resultIf you run the code again, you will probably see something like this:Code 4.6:[1.0, 1.1, 1.2100000000000002, 1.3310000000000004, 1.4641000000000006,1.6105100000000008, 1.771561000000001, 1.9487171000000014,2.1435888100000016, 2.357947691000002, 2.5937424601000023,2.853116706110003, 3.1384283767210035, 3.4522712143931042,3.797498335832415, 4.177248169415656, 4.594972986357222,5.054470284992944, 5.559917313492239, 6.115909044841463,6.72749994932561, 7.400249944258172, 8.140274938683989,8.954302432552389, 9.849732675807628, 10.834705943388391,11.91817653772723, 13.109994191499954, 14.420993610649951,15.863092971714948, 17.449402268886445]We see that the value of x certainly grew. But just staring at those numbers won’t give usmuch information about how it grew. We should visualize these numbers to observe thegrowth process in a more intuitive manner.To create a visual plot, we will need to use the matplotlib library 1 . Here we use itspylab environment included in matplotlib. Pylab provides a MATLAB-like working environmentby bundling matplotlib’s plotting functions together with a number of frequentlyused mathematical/computational functions (e.g., trigonometric functions, random numbergenerators, etc.). To use pylab, you can add the following line to the beginning of yourcode 2 :1 It is already included in Anaconda and Enthought Canopy. If you are using a different distribution ofPython, matplotlib is freely available from http://matplotlib.org/.2 Another way to import pylab is to write “import pylab” instead, which is recommended by moreprogramming-savvy people. If you do this, however, pylab’s functions have to have the prefix pylab addedto them, such as pylab.plot(result). For simplicity, we use “from pylab import *” throughout this textbook.