(a) Let c = 3. Find the critical points and the corresponding eigenvalues. (b) Plot the

Chapter 9, Problem 14

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(a) Let c = 3. Find the critical points and the corresponding eigenvalues. (b) Plot the trajectory starting at the point (1, 0, 2). Observe that the limit cycle now consists of two loops before it closes; it is often called a 2-cycle. (c) Plot x, y, or z versus t and show that the period T2 of motion on the 2-cycle is very nearly double the period T1 of the simple limit cycle in 12. There has been a period-doubling bifurcation of cycles for a certain value of c between 1.3 and 3.