Introduction to the Modeling and Analysis of Complex Systems

5.2. PHASE SPACE VISUALIZATION OF CONTINUOUS-STATE DISCRETE-TIME... 65Three-dimensional systems can also be visualized in a similar manner. For example,let’s try visualizing the following three-dimensional difference equation model:x t = 0.5x + y (5.14)y t = −0.5x + y (5.15)z t = −x − y + z (5.16)Plotting in 3-D requires an additional matplotlib component called Axes3D. A samplecode is given in Code 5.2. Note the new import Axes3D line at the beginning, as wellas the two additional lines before the for loops. This code produces the result shown inFig. 5.2.Code 5.2: phasespace-drawing-3d.pyfrom pylab import *from mpl_toolkits.mplot3d import Axes3Ddef initialize(x0, y0, z0):global x, y, z, xresult, yresult, zresultx = x0y = y0z = z0xresult = [x]yresult = [y]zresult = [z]def observe():global x, y, z, xresult, yresult, zresultxresult.append(x)yresult.append(y)zresult.append(z)def update():global x, y, z, xresult, yresult, zresultnextx = 0.5 * x + ynexty = -0.5 * x + ynextz = - x - y + zx, y, z = nextx, nexty, nextz