% Sheet 10 Exercise 3 (Lorenz)

% (3)

u0 = [1 2 3];
p = [10 8/3 28];

[t,u] = ode45(@LorenzModel, [0,7], u0, [], p);

plot(t,u)
% transient spike, steady state oscillations


% (4)
% Typo: Replace 7 by 100

u0 = 100*(rand(3,1)-0.5);
[t,u] = ode45(@LorenzModel, [0,100], u0, [], p);
v = u(find(t>10),:);

plot3(v(:,1), v(:,2), v(:,3));
title('The Lorenz attractor');
xlabel('x'), ylabel('y'), zlabel('z')