Introduction to the Modeling and Analysis of Complex Systems

4.4. SIMULATING DISCRETE-TIME MODELS WITH MULTIPLE VARIABLES 47global x, y, xresult, yresultxresult.append(x)yresult.append(y)def update():global x, y, xresult, yresultx = 0.5 * x + yy = -0.5 * x + yinitialize()for t in xrange(30):update()observe()plot(xresult, ’b-’)plot(yresult, ’g--’)show()What I did in this code is essentially to repeat things for both x and y. Executing two plotcommands at the end produces two curves in a single chart. I added the ’b-’ and ’g--’options to the plot functions to draw xresult in a blue solid curve and yresult in a greendashed curve. If you run this code, it produces a decent result (Fig. 4.2), so things mightlook okay. However, there is one critical mistake I made in the code above. Can you spotit? This is a rather fundamental issue in complex systems simulation in general, so we’dbetter notice and fix it earlier than later. Read the code carefully again, and try to findwhere and how I did it wrong.Did you find it? The answer is that I did not do a good job in updating x and y simultaneously.Look at the following part of the code:Code 4.12:x = 0.5 * x + yy = -0.5 * x + yNote that, as soon as the first line is executed, the value of x is overwritten by its newvalue. When the second line is executed, the value of x on its right hand side is alreadyupdated, but it should still be the original value. In order to correctly simulate simultaneousupdating of x and y, you will need to do something like this: