Solved: 6 through 10 suggest some further investigations of the Lorenz equations.For

Chapter 9, Problem 9

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6 through 10 suggest some further investigations of the Lorenz equations.For certain r intervals, or windows, the Lorenz equations exhibit a period-doubling propertysimilar to that of the logistic difference equation discussed in Section 2.9. Carefulcalculations may reveal this phenomenon.(a) One period-doubling window contains the value r = 100. Let r = 100 and plot thetrajectory starting at (5, 5, 5) or some other initial point of your choice. Does the solutionappear to be periodic? What is the period?(b) Repeat the calculation in part (a) for slightly smaller values of r.When r = 99.98, youmay be able to observe that the period of the solution doubles. Try to observe this resultby performing calculations with nearby values of r.(c) As r decreases further, the period of the solution doubles repeatedly. The next perioddoubling occurs at about r = 99.629. Try to observe this by plotting trajectories for nearbyvalues of r.