Introduction to the Modeling and Analysis of Complex Systems

258 CHAPTER 13. CONTINUOUS FIELD MODELS I: MODELINGglobal a, b, nexta, nextbfor x in xrange(n):for y in xrange(n):# state-transition functionaC, aR, aL, aU, aD = a[x,y], a[(x+1)%n,y], a[(x-1)%n,y], \a[x,(y+1)%n], a[x,(y-1)%n]bC, bR, bL, bU, bD = b[x,y], b[(x+1)%n,y], b[(x-1)%n,y], \b[x,(y+1)%n], b[x,(y-1)%n]bLapNum = bR + bL + bU + bD - 4 * bCnexta[x,y] = aC + mu_a * ((aR-aL)*(bR-bL)+(aU-aD)*(bU-bD)+4*aC*bLapNum) * Dt/(4*Dh**2)nextb[x,y] = bC + mu_b * bLapNum * Dt/(Dh**2)a, nexta = nexta, ab, nextb = nextb, bimport pycxsimulatorpycxsimulator.GUI(stepSize = 50).start(func=[initialize, observe, update])Note that the observe function now uses subplot to show two scalar fields for a and b.The result is shown in Fig. 13.16.0a0b0a0b0a0b2020202020204040404040406060606060608080808080800 20 40 60 800 20 40 60 800 20 40 60 800 20 40 60 800 20 40 60 800 20 40 60 80Figure 13.16: Visual output of Code 13.7. Time flows from left to right.Exercise 13.15 Modify Code 13.7 so that both species diffuse and try to escapefrom each other. Run simulations to see how the system behaves.