今天画个蝶，一个Lorenz彩蝶|混沌系统的初始参数敏感性

clc

close all

clear

syms x(t)

fun = @(t, x)[-10*x(1)+10*x(2); 28*x(1)-x(2)-x(1)*x(3); x(1)*x(2)-8/3*x(3)];

tspan = [0 20];

[t1, x1] = ode45(fun, tspan, [10, -10, -10]);

plot3(x1(:, 1), x1(:, 2), x1(:, 3), 'LineWidth', 1.5);

hold on;

[t2, x2] = ode45(fun, tspan, [10.001, -10, -10]);

plot3(x2(:, 1), x2(:, 2), x2(:, 3), 'LineWidth', 1.5);

[t3, x3] = ode45(fun, tspan, [10.002, -10, -10]);

plot3(x3(:, 1), x3(:, 2), x3(:, 3), 'LineWidth', 1.5);

legend('\sigma = 10', '\sigma = 10.001', '\sigma = 10.002')

grid on;

hold off;

caz = -60;

cel = 0;

view(caz, cel);

xlim([-30, 30]);

ylim([-30, 40]);

zlim([-20, 60]);

for n = 1:70

  caz = caz + 1;

  view(caz,cel);

  drawnow

end

plot(t1, x1(:, 1), t2, x2(:, 1), t3, x3(:, 1))

legend('x11', 'x21', 'x31')