clear;


global a k

a = .4;
k = 10;



dt=.5;
Tf=10;

T=0:dt:Tf;


x0=2;

X=zeros(1,length(T));
Xrk4=zeros(1,length(T));
Xpji=zeros(1,length(T));

% figure(2)
% plot(T,X)

X(1)=x0;


for s=2:length(T)

    X(s) = X(s-1) + dt * flogi(X(s-1)) ;
    
end


Xrk4(1)=x0;
for s=2:length(T)
    
    x = Xrk4(s-1);    
    k1 = flogi(x);
    k2 = flogi(x+k1*dt/2);
    k3 = flogi(x+k2*dt/2);
    k4 = flogi(x+k3*dt);
    
    
    Xrk4(s) = Xrk4(s-1) + dt * (k1+2*k2+2*k3+k4)/6;
end

Xpji(1) = x0;
for s=2:length(T)
    
    x = Xpji(s-1);    
     
    
    Xpji(s) = exp(a*(1-x/k)*dt)*x;
end



Tth = linspace(0,Tf,1001);
Xtheor = x0*k*exp(a*Tth) ./ (x0*(exp(a*Tth)-1)+k);

figure(2)
plot(T,X,'.b',Tth,Xtheor,'k',T,Xrk4,'.r',T,Xpji,'.y')