Introduction to the Modeling and Analysis of Complex Systems

16.2. SIMULATING DYNAMICS ON NETWORKS 333def update():global glistener = rd.choice(g.nodes())speaker = rd.choice(g.neighbors(listener))g.node[listener][’state’] = g.node[speaker][’state’]import pycxsimulatorpycxsimulator.GUI().start(func=[initialize, observe, update])See how simple the update function is! This simulation takes a lot more steps for thesystem to reach a homogeneous state, because each step involves only two nodes. It isprobably a good idea to set the step size to 50 under the “Settings” tab to speed up thesimulations.Exercise 16.2 Revise the code above so that you can measure how many stepsit will take until the system reaches a consensus (i.e., homogenized state). Thenrun multiple simulations (Monte Carlo simulations) to calculate the average timelength needed for consensus formation in the original voter model.Exercise 16.3 Revise the code further to implement (1) the reversed and (2) theedge-based voter models. Then conduct Monte Carlo simulations to measure theaverage time length needed for consensus formation in each case. Compare theresults among the three versions.Discrete state/time models (2): Epidemic model The second example of discretestate/time dynamical network models is the epidemic model on a network. Here we considerthe Susceptible-Infected-Susceptible (SIS) model, which is even simpler than theSIR model we discussed in Exercise 7.3. In the SIS model, there are only two states:Susceptible and Infected. A susceptible node can get infected from an infected neighbornode with infection probability p i (per infected neighbor), while an infected node can recoverback to a susceptible node (i.e., no immunity acquired) with recovery probability p r(Fig. 16.3). This setting still puts everything in binary states like in the earlier examples,so we can recycle their codes developed above.