% rickerbif.m - this MATLAB file simulates the 
% ricker difference equation x(n+1)=x(n)*exp(r*(1-x(n)/K))
% and carries out a bifurcation analysis by varying r.
% 200 different values of a are used between the 
% ranges rmin and rmax set by the user. A bifurcation
% plot is drawn by showing the last 250 points of
% a sequence of 1000 simulated points for each
% value of r. The initial condition is fixed at x0=K

b=4;     
rmin=3.2;  %rmin = minimum intrinsic rate of growth
rmax=3.6; % rmax = maximum intrinsic rate of growth
x0=b/2;   %initial population x0 of host   


n=1000;  
jmax=500;
t=zeros(jmax+1,1);
z=zeros(jmax+1,250);
del=(rmax-rmin)/jmax;
for j=1:jmax+1
x=zeros(n+1,1);
x(1)=x0;
t(j)=(j-1)*del+rmin;
r=t(j);
for i=1:n
x(i+1)=r*x(i)/(1+x(i)^b);   %defines the difference equation for which the bifurcation diagram is being created
if (i>750) 
   z(j,i-750)=x(i+1);
   end
end
end
plot(t,z,'b.','MarkerSize',4)
xlabel('r','FontSize',10), ylabel('Abundance','FontSize',10)
title('Bifurcation diagram for the Bellows model')