% Some code to study Problem 3, Homework 3, Math 5110, Fall 2005

% Set values for the parameters
A=1/3;
alpha=1/2;
gamma=2/3;

% Input number of steps
nsteps = 30;

% Input some initial conditions (low values of both c and q)
c0=0.1;
q0=0.1;

% Input the function for h with n=2 (to be varied by hand)
h = inline('c^2/(1+c^2)','c')

% Initialize vectors to save the results
c=c0
q=q0

% Run a loop 
for i=1:(nsteps-1),
  c(i+1)=(1-q(i))*(c(i)+A)+q(i)*gamma;
  q(i+1)=alpha*q(i)+(1-alpha)*h(c(i));
end

%Plot up the results as functions of time
plot(1:nsteps,c,'r',1:nsteps,q,'b')

%Plot up c as a function of q
plot(q,c,'r')

% Now you can go back and change n to see if and when the equilibrium 
% becomes unstable