Exercise G. Below we have reproduced the bifurcation diagram of the spruce budworm model. 0.6 t...

 

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Exercise G. Below we have reproduced the bifurcation diagram of the spruce budworm model. 0.6 t 0.5 0.4 0.3 0.2 T 0.1 10 20 30 40 a) For each of the following (k, r) points in the diagram, determine how many equilibrium points the system has, what the stability of each equilibrium point is, and whether the X-value of the equilibrium point (s) is high, medium, or low. The points are: (k, r) = (5,0.5), (k,r) = (15, 0.6), and (k, r) = (40, 0.4). b) How many bifurcation(s) occur(s) when k = 10. For each bifurcation, indicate the approximate value of r. c) Same question when r = 0.1 (give the approximate value(s) of k). Exercise G. Below we have reproduced the bifurcation diagram of the spruce budworm model. 0.6 t 0.5 0.4 0.3 0.2 T 0.1 10 20 30 40 a) For each of the following (k, r) points in the diagram, determine how many equilibrium points the system has, what the stability of each equilibrium point is, and whether the X-value of the equilibrium point (s) is high, medium, or low. The points are: (k, r) = (5,0.5), (k,r) = (15, 0.6), and (k, r) = (40, 0.4). b) How many bifurcation(s) occur(s) when k = 10. For each bifurcation, indicate the approximate value of r. c) Same question when r = 0.1 (give the approximate value(s) of k).