Introduction to the Modeling and Analysis of Complex Systems

70 CHAPTER 5. DISCRETE-TIME MODELS II: ANALYSISx maxx t = f(x t-1 )x tx t = x t-1x minx minx t-1x maxFigure 5.5: Drawing a cobweb plot (2).5. Repeat the steps above to see where the system eventually goes (Fig. 5.8).6. Once you get used to this process, you will notice that you don’t really have to toucheither axis. All you need to do to draw a cobweb plot is to bounce back and forthbetween the curve and the line (Fig. 5.9)—move vertically to the curve, horizontallyto the line, and repeat.Exercise 5.5 Draw a cobweb plot for each of the following models:• x t = x t−1 + 0.1, x 0 = 0.1• x t = 1.1x t−1 , x 0 = 0.1Exercise 5.6 Draw a cobweb plot of the following logistic growth model with r = 1,K = 1, N 0 = 0.1:N t = N t−1 + rN t−1 (1 − N t−1 /K) (5.17)