Chapter 3.6, Problem 21P

Consider the system in Example $1$. Draw a component plot of $x$ versus $t$ for several of the periodic solutions in the vicinity of the origin.

From the plots in part (a), estimate the period and amplitude of each of the solutions. Is the period the same regardless of the amplitude? If not, how is the period related to the amplitude?

Example $1$:

Consider the system $\frac{dx}{dt}=x-y,\frac{dy}{dt}=2x-y-x^2$.