% Kartik's MATLAB session with the Lorenz model (chaos!)
% Consider the system
% dx/dt = 10*(-x+y)
% dy/dt = 28*x-y-x*z
% dz/dt = -10/3*z + x*y
% Let us examine this system for the following initial conditions
% [x0,y0,z0] = [5,5,5] and [x0,y0,z0] = [5.01,5,5]
% Our system of differential equations is in the file
% lorenzfunc.m (look at the calling sequence in this file!)
% We will solve the initial value problem using MATLAB's ode45
% function
% Kartik's MATLAB session Nov 30, 2005.

[t,x] = ode45(@lorenzfunc,[0 20],[5 5 5]');
figure(1)
plot(t,x(:,1));
% Let us label the axes and the plot
legend('Initial condition [5 5 5]');
xlabel('time t');
ylabel('variable x');
[t,x] = ode45(@lorenzfunc,[0 20],[5.01 5 5]');
figure(2);
plot(t,x(:,1));
legend('Initial condition [5.01 5 5]');
xlabel('time t');
ylabel('variable x');
figure(3);
plot(x(:,1),x(:,2));
% Label the axes again
xlabel('x');
ylabel('y');
figure(3);
plot(x(:,1),x(:,3));
% Label the axes again
xlabel('x');
ylabel('z');