Differential Equations Problem

A two-mode laser produces two dierent kinds of photons. The number of photons in the laser eld of each type are n1 and n2:

These vary in time and are governed by the DE system

n*1(n with dot on top) = G1*N*n1 - k1*n1

n*2(n with dot on top) = G2*N*n2 - k2*n2

where N(t) = N0 - alpha1*n1 - alpha2*n2

For a given experiment the parameters are given by G1 = 2; G2 = 1; alpha1 =

1;alpha2 = 2;k1 = 2;k2 = 2 and N0 = 4

(a) Find and classify all the equilibrium points and sketch the solutions in

the phase plane.

(b) What is the long term behaviour of the laser?