Introduction to the Modeling and Analysis of Complex Systems

64 CHAPTER 5. DISCRETE-TIME MODELS II: ANALYSISshow()Revised parts from the previous example are marked with ###. Here, the arange functionwas used to vary initial x and y values over [−2, 2] at interval 0.5. For each initial state, asimulation is conducted for 30 steps, and then the result is plotted in blue (the ’b’ optionof plot). The output of this code is Fig. 5.1, which clearly shows that the phase space ofthis system is made of many concentric trajectories around the origin.32101234 3 2 1 0 1 2 3 4Figure 5.1: Phase space drawn using Code 5.1.Exercise 5.4 Draw a phase space of the following two-dimensional differenceequation model in Python:x t = x t−1 + 0.1(x t−1 − x t−1 y t−1 ) (5.11)y t = y t−1 + 0.1(y t−1 − x t−1 y t−1 ) (5.12)(x > 0, y > 0) (5.13)