(a) Let c = 3.8. Find the critical points and the corresponding eigenvalues. (b) Plot

Chapter 9, Problem 15

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(a) Let c = 3.8. Find the critical points and the corresponding eigenvalues. (b) Plot the trajectory starting at the point (1, 0, 2). Observe that the limit cycle is now a 4-cycle. Find the period T4 of motion. Another period-doubling bifurcation has occurred for c between 3 and 3.8. (c) For c = 3.85 show that the limit cycle is an 8-cycle. Verify that its period is very close to eight times the period of the simple limit cycle in 12. Note: As c increases further there is an accelerating cascade of period-doubling bifurcations. The bifurcation values of c converge to a limit, which marks the onset of chaos.