function LogisticDifference

%Plots solutions to the nonlinear difference equation x_{n+1}=rx_n(1-x_n) where x=x_n and y=x_{n+1} 
t=100;           %total number of time steps
n=[0:1:t];      %sets n=0,1,2,...,t
x=[0:1:t];      %Establishes matrix dimensions, will be overwritten in the for loop


%Initial Condition
x0=.01;          

%Parameter
r=3.3;  
steadystate=(r-1)/r+n-n;

%Determines x_n in an iterative manner
for i=1:t+1
    if i==1;
        x(i)=x0;
    else 
        x(i)=r*x(i-1)*(1-x(i-1));
        i=i+1;
    end
end

x

%x1=(r+1)/(2*r)+(((r-3)*(r+1))^(1/2))/(2*r)+n-n;
%x2=(r+1)/(2*r)-(((r-3)*(r+1))^(1/2))/(2*r)+n-n;

%Plots solutions
plot(n,x,n,steadystate)
%plot(n,x,n,steadystate,n,x1,n,x2)
xlabel('n')
ylabel('x_n')
title('Plot of x_n as a function of n')