%  The Nicholson-Baily Model of Host-Parasatoid System
%
%	N(i+1) = lam*N(i)*exp(-a*P(i))
%	P(i+1) = c*N(i)*(1 - exp(-a*P(i))
%
%  To use: 
%  [X, xbar, J1] = NB(lam,a,c, x0,NTIME)
%
%  Output matrix X holds values of N and P in 1st and 2nd rows - NTIME
%  columns
% 
%  xbar = gives the non-zero steady state values of N and P
%
%  J1 = gives the Jacobian matrix evaluated at xbar
%
 function [x, xbar,J1] = NB(lam,a,c, x0,NTIME)

 x(:,1) = x0;
 for i =1:NTIME 
	x(1,i+1) = lam*x(1,i)*exp(-a*x(2,i));
	x(2,i+1) = c*x(1,i)*(1 - exp(-a*x(2,i)));
 end

  xbar(1) = lam*log(lam)/(a*c*(lam-1));
  xbar(2) = log(lam)/a;

 J1 = [1, -a*lam*xbar(1); 0, a*c*xbar(1)];

 return