6 through 10 suggest some further investigations of the Lorenz equations.. (a) Forr =

Chapter 9, Problem 8

(choose chapter or problem)

6 through 10 suggest some further investigations of the Lorenz equations.. (a) Forr = 21, plot x versust for the solutions starting at the initial points(3, 8, 0),(5, 5, 5),and (5, 5, 10). Use a t-interval of at least 0 t 30. Compare your graphs with those inFigure 9.8.4.(b) Repeat the calculation in part (a) forr = 22,r = 23, and r = 24. Increase the t intervalas necessary so that you can determine when each solution begins to converge to one ofthe critical points. Record the approximate duration of the chaotic transient in each case.Describe how this quantity depends on the value of r.(c) Repeat the calculations in parts (a) and (b) for values of r slightly greater than 24.Try to estimate the value of r for which the duration of the chaotic transient approachesinfinity.