% Lyapunov exponents of Lorenz
%
% Author：yujunjie
% Author's email: ustb03-07@yahoo.com.cn
%
function lorenzlp
Z1=[];
Z2=[];
Z3=[];
global a;
global b;
global r;
a=10;b=8/3;
for r=linspace(0,500,80);
y=[1;1;1;1;0;0;0;1;0;0;0;1];
lp=0;
for k=1:100
[T,Y] = ode45('Lorenz2', 1, y);
y = Y(size(Y,1),:);
y0 = [y(4) y(7) y(10);
y(5) y(8) y(11);
y(6) y(9) y(12)];
y0=GS(y0);
mod(1)=norm(y0(:,1));
mod(2)=norm(y0(:,2));
mod(3)=norm(y0(:,3));
lp = lp+log(abs(mod));
y0(:,1)=y0(:,1)/mod(1);
y0(:,2)=y0(:,2)/mod(2);
y0(:,3)=y0(:,3)/mod(3);
y(4:12) = y0';
end
lp=lp/100;
Z1=[Z1 lp(1)];
Z2=[Z2 lp(2)];
Z3=[Z3 lp(3)];
end
r=linspace(0,500,80);
plot(r,Z1,'-',r,Z2,'-',r,Z3,'-');
title('Lyapunov exponents of Lorenz')
xlabel('parameter r'),ylabel('lyapunov exponents')
grid on
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