For certain r intervals, or windows, the Lorenz equation
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For certain r intervals, or windows, the Lorenz equations exhibit a period-doubling property. Careful calculations may r
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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. Letr = 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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