Introduction to the Modeling and Analysis of Complex Systems

13.5. SIMULATION OF CONTINUOUS FIELD MODELS 257Below is a sample code for simulating this PDE model starting with an initial configurationwith two peaks, one for a and the other for b:Code 13.7: transport-ca-escaping.pyimport matplotlibmatplotlib.use(’TkAgg’)from pylab import *n = 100 # size of grid: n * nDh = 1. / n # spatial resolution, assuming space is [0,1] * [0,1]Dt = 0.01 # temporal resolutionmu_a = 0.001 # mobility of species amu_b = 0.001 # mobility of species bxvalues, yvalues = meshgrid(arange(0, 1, Dh), arange(0, 1, Dh))def initialize():global a, b, nexta, nextb# initial configurationa = exp(-((xvalues - 0.45)**2 + (yvalues - 0.45)**2) / (0.3**2))b = exp(-((xvalues - 0.55)**2 + (yvalues - 0.55)**2) / (0.1**2))nexta = zeros([n, n])nextb = zeros([n, n])def observe():global a, b, nexta, nextbsubplot(1, 2, 1)cla()imshow(a, vmin = 0, vmax = 1)title(’a’)subplot(1, 2, 2)cla()imshow(b, vmin = 0, vmax = 1)title(’b’)def update():