Use Matlab make a bifurcation diagram like Figure 2.16. The code uses parameter b = -0.3 and a ranging from 0 to 2 by increments of da= 0.001. For each value of the parameter a, the code chooses the initial point (0, 2) and calculates its 1 orbit under the Henon map to step 104. It then plots the last N iterates (x-coordinates of the orbit) where N is small enough to allow the orbit to settle down to the attracting set (and not crush the graphics card in your computer). 2.5 -2.5 0 1.25 Figure 2.16 Bifurcation diagram for the Hnon map, b = 0.4. Each vertical slice shows the projection onto the x-axis of an attractor for the map for a fixed value of the parameter a. (a) Is the picture different if the y-coordinate is plotted instead? (b) Make an additional diagram varying the parameter a from 1.925 to 1.975 by increments of da = 0.0001. Are there any periodic windows? For which values of a? (c) Generate an estimate of Feigenbaums constant for the period-doubling cascade using a sequence of bifurcations up to period-64. You may need to make da smaller in order to resolve when a bifurcation takes place. Why doesn't your estimate approach 4.669...? Use Matlab make a bifurcation diagram like Figure 2.16. The code uses parameter b = -0.3 and a ranging from 0 to 2 by increments of da= 0.001. For each value of the parameter a, the code chooses the initial point (0, 2) and calculates its 1 orbit under the Henon map to step 104. It then plots the last N iterates (x-coordinates of the orbit) where N is small enough to allow the orbit to settle down to the attracting set (and not crush the graphics card in your computer). 2.5 -2.5 0 1.25 Figure 2.16 Bifurcation diagram for the Hnon map, b = 0.4. Each vertical slice shows the projection onto the x-axis of an attractor for the map for a fixed value of the parameter a. (a) Is the picture different if the y-coordinate is plotted instead? (b) Make an additional diagram varying the parameter a from 1.925 to 1.975 by increments of da = 0.0001. Are there any periodic windows? For which values of a? (c) Generate an estimate of Feigenbaums constant for the period-doubling cascade using a sequence of bifurcations up to period-64. You may need to make da smaller in order to resolve when a bifurcation takes place. Why doesn't your estimate approach 4.669