DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS

3rd Edition

ISBN: 9781119764564

Author: BRANNAN

Publisher: WILEY

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Textbook Question

Chapter 7.6, Problem 8P

For certain r intervals, or windows, the Lorenz equations exhibit a period-doubling property. Careful calculations may reveal this phenomenon.

(a) One period-doubling window contains the value r = 100 . Let r = 100 and plot the trajectory starting at ( 5 , 5 , 5 ) or some other initial point of your choice. Does the solution appear to be periodic? What is the period?

(b) Repeat the calculation in part (a) for slightly smaller values of r . When r ≅ 99.98 , you may be able to observe that the period of the solution doubles. Try to observe this result by performing calculations with nearby values of r .

(c) As r decreases further, the period of the solution doubles repeatedly. The next period doubling occurs at about r ≅ 99.629 . Try to observe this by plotting trajectories for nearby values of r .

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Chapter 7.6, Problem 7P

Chapter 7.6, Problem 9P

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DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS

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