Introduction to the Modeling and Analysis of Complex Systems

16.2. SIMULATING DYNAMICS ON NETWORKS 345import pycxsimulatorpycxsimulator.GUI().start(func=[initialize, observe, update])Figure 16.8 shows a typical simulation run. The dynamics of this simulation can be bettervisualized if you increase the step size to 50. Run it yourself, and see how the inherentlydiverse nodes get self-organized to start a synchronized marching. Do you see any spatialpatterns there?Figure 16.8: Visual output of Code 16.8. Time flows from left to right.Exercise 16.8 It is known that the level of synchronization in the Kuramoto model(and many other coupled oscillator models) can be characterized by the followingmeasurement (called phase coherence):1 ∑r =e iθ i(16.13)∣n∣iHere n is the number of nodes, θ i is the state of node i, and i is the imaginaryunit (to avoid confusion with node index i). This measurement becomes 1 if all thenodes are in perfect synchronization, or 0 if their phases are completely randomand uniformly distributed in the angular space. Revise the simulation code sothat you can measure and monitor how this phase coherence changes during thesimulation.Exercise 16.9topologies:Simulate the Kuramoto model on each of the following network