Chapter 7.P3, Problem 2P

a) Let $c=1.3$. Find the critical points and the corresponding eigenvalues. What conclusions, if any, can youdraw from this information?

b) Plot the trajectory starting at the origin. What is the limiting behavior of this trajectory? To see the limiting behaviour clearly, you may wish to choose a $t$-interval for your plot sothat the initial transients are eliminated.

c) Choose one or two other initial points and plot the corresponding trajectories. Are the limiting behavior(s) the sameas in part (b)?

d) Observe that there is a limit cycle whose basin of attraction is fairly large (although not all of $xyz$-space). Draw a plot of $x,y,$ or $z$ versus $t$ and estimate the period of motion around the limit cycle.