1. (22 points) Consider the 1D system x=rx(120x)1+x2x2 (a) Use XPP to plot a bifurcation diagram. Use ymin=-0.5, ymax =20, xmin =0.5, xmax=5. (b) Assume x represents the number of budworms, measured in millions. Explain what happens to the population in the long run if the growth rate is r=0.3. (c) Explain what happens to the population in the long run if the growth rate is r=3. (d) Starting at the stable fixed point when r=0.3, describe what happens to the population as the parameter r is slowly increased. At what value of r is there a significant change in the population? What happens to the population if you keep increasing r beyond this value? (e) Now slowly decrease r from where it ended up in part (d). The population remains on the large amplitude branch until when? What happens at this point? 1. (22 points) Consider the 1D system x=rx(120x)1+x2x2 (a) Use XPP to plot a bifurcation diagram. Use ymin=-0.5, ymax =20, xmin =0.5, xmax=5. (b) Assume x represents the number of budworms, measured in millions. Explain what happens to the population in the long run if the growth rate is r=0.3. (c) Explain what happens to the population in the long run if the growth rate is r=3. (d) Starting at the stable fixed point when r=0.3, describe what happens to the population as the parameter r is slowly increased. At what value of r is there a significant change in the population? What happens to the population if you keep increasing r beyond this value? (e) Now slowly decrease r from where it ended up in part (d). The population remains on the large amplitude branch until when? What happens at this point