8.1.11 u = a(1 u) uv 2 There is a xed point at (1, 0) for all a and k . Nullclines curves are given by u= a a + v2 and u= a+k v v = uv 2 (a + k )v
Figure 1: Nullcline Curves as the parameters are varied These curves intersect when
a+k a = 2 a+v v
(0.1)
s
Harmonic Oscillator (pendulum)
Problem 1. In Strogatz Chapter 6 it was shown that the origin is a nonlinear
center for the pendulum example. Let
x + sin x = 0.
(a) Can you prove stability of the origin using linearization? Use an appropriate Liapunov fun