a. Use a numerical method (and a computer) to solve dR dt

= sin(R), R(0) = 1, for 0 ≤ t ≤ 10, and plot the solution.

b. What happens if you change the initial conditions? Can you see why?

c. Can you predict the final value of R as t → ∞? (Hint:

as t → ∞ the solution is getting flatter and flatter, which means that R 0

(t) must be going to zero.)

Another hint: use a qualitative analysis like that in the previous chapter to determine which of the steady states are sources, and which are sinks. Why does this matter?