How to Modify MATLAB Code for a New Cobweb Plot Equation?

[fauboca]

I found some Matlab code that works. However, I am not sure how to alter it for my needs.

How can I make the code work for this:

$$N_{t+1} = \frac{(1+r)N_t}{1+rN_t}$$

What needs to be changed?

%%% MAKES A COBWEB PLOT FOR A LOGISTIC MAP

% compute trajectory
a=3.0;          % parameter
x0=0.2;         % Initial condition 
N=40;           % Number of iterations
x(1) = x0;    
for ic=1:N
 x(ic+1) = a*x(ic)*(1-x(ic)); 
end




% plot the map function and the line y=x
clf;
t = 0:0.01:1;
plot(t,a*(t.*(1-t))); hold on;
 axis('square'); axis([0 1 0 1]);
 set(gca,'XTick',(0:0.1:1),'YTick',(0:0.1:1))
 grid on;


 fplot('1*y',[0 1],'r');



%%%%%% STEP 3: PLOT COBWEB
 line([x(1) x(1)],[0 x(2)],'Color','g') 
  plot(x(1), x(1),'ko');
 for ic=1:N-1
  line([x(ic) x(ic+1)],[x(ic+1) x(ic+1)],'Color','g')  
  line([x(ic+1) x(ic+1)],[x(ic+1) x(ic+2)],'Color','g')
  plot(x(ic+1), x(ic+1),'ko');
 end
 line([x(N) x(N+1)],[x(N+1) x(N+1)],'Color','g')
 
   %%%%%% STEP 4: SIGN THE PLOT
 at=text(0.1,0.82,['a=',num2str(a)]); set(at,'FontSize',12);

 

[lippyka]

set(at,'HorizontalAlignment','right'); at=text(0.1,0.90,['x_0=',num2str(x0)]); set(at,'FontSize',12); set(at,'HorizontalAlignment','right'); at=text(0.1,0.98,['N=',num2str(N)]); set(at,'FontSize',12); set(at,'HorizontalAlignment','right'); To make this code work for your equation:$$N_{t+1} = \frac{(1+r)N_t}{1+rN_t}$$you need to change the code as follows:% compute trajectoryr=3.0; % parameterx0=0.2; % Initial condition N=40; % Number of iterationsx(1) = x0; for ic=1:N x(ic+1) = (1+r)*x(ic)/(1+r*x(ic)); end% plot the map function and the line y=xclf;t = 0:0.01:1;plot(t,(1+r)*(t./(1+r*t))); hold on; axis('square'); axis([0 1 0 1]); set(gca,'XTick',(0:0.1:1),'YTick',(0:0.1:1)) grid on; fplot('1*y',[0 1],'r');%%%%%% STEP 3: PLOT COBWEB line([x(1) x(1)],[0 x(2)],'Color','g') plot(x(1), x(1),'ko'); for ic=1:N-1 line([x(ic) x(ic+1)],[x(ic+1) x(ic+1)],'Color