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?