Figure 3.39: At selected values of the parameter a (the horizontal axis), we construct a one- dimensional state space shown vertically with its equilibrium points and their stability indicated. I Now if we imagine many many of these state spaces stacked side by side, we can draw lines connecting the equilibrium points at adjacent a values. This is the bifurcation diagram (Figure 3.40). X X - Stable - . unstable 0+ 300 500 1000(-k] 1500 300 500 1000(-kj 1500 Figure 3.40: A bifurcation diagram of the equation X* = 0.1X(=-1)(1-#). Solid lines represent stable equilibria, while dashed lines represent unstable ones. The horizontal axis of this figure shows values of a, and the vertical axis shows values of X. For each value of a, the diagram shows the corresponding equilibrium points. (It is common to show stable equilibria as solid lines and unstable ones as dashed lines.) Exercise 3.6.2 Use the bifurcation diagram in Figure 3.40 to find the equilibrium population levels at a = 600, a = 900, and a = 1200. Describe the stability of each equilibrium point