lp_qi=zeros(1,4);

%global a b c d e f;
%a = 50 c = 13, d = 8, e = 33, f = 30
for b=linspace(16,27,200);
    [T,Res]=lyapunov(4,@qi_hyper,@ode45,0,0.1,100,[10 8 3 2],10);
    lp_qi=[lp_qi;Res(end,:)];
end

lp_qi(1,:)=[]
b=linspace(16,27,200);
plot(b,lp_qi(:,1),'-',b,lp_qi(:,2),'-',b,lp_qi(:,3),'-',b,lp_qi(:,4),'-');
title('Lyapunov exponents of qi hyperchaotic system')
xlabel('parameter b'),
ylabel('lyapunov exponents')
grid on

qi_hyper_lyaDim=3+(lp_qi(:,1)+lp_qi(:,2)+lp_qi(:,3))./abs(lp_qi(:,4))  %分形維數(shù)
figure;
plot(b,qi_hyper_lyaDim);
title('The Lyapunov dimension of a 4-D hyperchaotic system')
xlabel('parameter b'),
ylabel('Lyapunov dimension')
grid on