%% obraz fazowy kultywatora

%% du/dtau=f=lambda1*c/(1+c)*u-u;
%% dc/dtau=g=-c/(1+c)*u+lambda2-c;

lambda1=2;
lambda2=2;
%% teraz f=0
u=[0.01:0.01:5];

vf2=u./(u.*(lambda1-1));
%% teraz g=0

vg1=(-(1+u-lambda2)+sqrt((1+u-lambda2).^2+4*lambda2))/2;
vg2=(-(1+u-lambda2)-sqrt((1+u-lambda2).^2+4*lambda2))/2;
clf;
hold on;
plot([0,0],[0,lambda2],'-g',u,vf2,'-c',u,vg1,'-r',u,vg2,'-b');
[u c]=meshgrid(0.1:0.1:5,0.1:0.1:2);
f=lambda1*c./(1+c).*u-u;
g=-c./(1+c).*u+lambda2-c;
quiver(u,c,f,g,2);
hold off;