P1. Logistic differential equation:
dx/dt = 5x - 0.1(x^2)
a) Describe dynamics as t goes to infinity?
b) Write the finite difference approximation to the equation used in the Euler method?
c) For what step size values does the diff. approximation approach a fixed point as n goes to infinity? What is the fixed point?
d) For what step size values does the diff. approximation exhibit oscillations as n goes to infinity?