function MichMent
clear;
close;
time_end=3;
K=0.5;
lambda=1.0;
epsilon=0.05;
u=0.01:0.01:1; 
tau=(1-u-K*log(u))/lambda;

options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4]);
[T,Y] = ode45(@mmeoms,[0 time_end],[1.0 0.0],options);
plot(T,Y(:,1),'-b',T,Y(:,2),'--g','LineWidth',3);
axis([0 time_end 0.0 1.0]);
hold on;
pause;
plot(T,Y(:,1)./(K+Y(:,1)),'-r','LineWidth',3);
pause;
plot(tau,u,'--r','LineWidth',3);
pause;
hold off;
close;

function dy=mmeoms(t,y)
%  returns the coupled odes
    dy=zeros(2,1);
    dy(1)=-y(1)+(y(1)+K-lambda)*y(2);
    dy(2)=(y(1)-(y(1)+K)*y(2))/epsilon;
end
end







