clear, set(0,'DefaultFigureWindowStyle','docked')
x0 = 1e-2; T = 1; lambda = 500;
f =@(t,y) lambda*y.^2.*(1-y);

opts = odeset('reltol', 1e-8, 'abstol', 1e-8);
[t, z] = ode45(f, [0, T], x0, opts);

figure;
subplot(2,1,1), plot(t,z(:,1)); title('ode45')
subplot(2,1,2), semilogy(t(2:end), diff(t)); title('stepsize')
pause
opts = odeset('reltol', 1e-8, 'abstol', 1e-8);
[t, z] = ode23s(f, [0, T], x0, opts);

figure;
subplot(2,1,1), plot(t,z(:,1)); title('ode23s')
subplot(2,1,2), semilogy(t(2:end), diff(t)); title('stepsize')