%
%hyperbolic.m - this MATLAB file solves the 
%discrete first order non-linear hyperbolic difference
% equation often used as a 
%discrete analog of the continuous logistic
% growth model x(i+1)=k*x(i)/(b+x(i))
%and the user is prompted to read in the value
% of k and b to use as well as the initial value
% x0 and the time interval over which to run the 
% simulation.
!c:
s=1;
while s>0;
k=input('input parameter k:    ')
b=input('input parameter b:    ')
x0=input('input initial population x0:     ')
n=input('end of time interval b:     ')
x=zeros(n+1,1);
t=zeros(n+1,1);
x(1)=x0;
for i=1:n
t(i)=i-1;
x(i+1)=k*x(i)/(b+x(i));
end
t(n+1)=n;
plot(t,x,t,x,'o'),pause
s=input('Do you want to stop - if so enter 0')
end