Introduction to the Modeling and Analysis of Complex Systems

4.3. SIMULATING DISCRETE-TIME MODELS WITH ONE VARIABLE 41Finally, we need to program the updating part. This is where the actual simulationoccurs. This can be implemented in another function:Code 4.3:def update():global x, resultx = a * xNote that the last line directly overwrites the content of symbol x. There is no distinctionbetween x t−1 and x t , but this is okay, because the past values of x are stored in the resultslist in the observe function.Now we have all the three crucial components implemented. We also need to addparameter settings to the beginning, and the iterative loop of updating at the end. Here,let’s let a = 1.1 so that the value of x increases by 10% in each time step. The completedsimulation code looks like this:Code 4.4:a = 1.1def initialize():global x, resultx = 1.result = [x]def observe():global x, resultresult.append(x)def update():global x, resultx = a * xinitialize()for t in xrange(30):update()observe()Here we simulate the behavior of the system for 30 time steps. Try running this code in