6592cd058d
git-subtree-dir: octive-lean git-subtree-mainline:fd3d42ae33git-subtree-split:4b6fcec565
53 lines
1.2 KiB
Matlab
53 lines
1.2 KiB
Matlab
% Example 3: Lorenz system
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% x' = -sigma*x + sigma*y
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% y' = rho*x - y - x*z
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% z' = -beta*z + x*y
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% Slide uses sigma = 10, rho = 70, beta = 8/3, x0=y0=z0=1.
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sigma = 10.0;
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rho = 70.0;
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beta = 8.0/3.0;
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n = 5000;
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t0 = 0; tf = 25.0;
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h = (tf - t0) / n;
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t = zeros(1, n+1);
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xs = zeros(1, n+1);
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ys = zeros(1, n+1);
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zs = zeros(1, n+1);
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xs(1) = 1.0;
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ys(1) = 1.0;
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zs(1) = 1.0;
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for i = 1:n
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ti = t(i); xi = xs(i); yi = ys(i); zi = zs(i);
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k1x = -sigma*xi + sigma*yi;
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k1y = rho*xi - yi - xi*zi;
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k1z = -beta*zi + xi*yi;
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ax = xi + h/2*k1x; ay = yi + h/2*k1y; az = zi + h/2*k1z;
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k2x = -sigma*ax + sigma*ay;
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k2y = rho*ax - ay - ax*az;
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k2z = -beta*az + ax*ay;
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ax = xi + h/2*k2x; ay = yi + h/2*k2y; az = zi + h/2*k2z;
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k3x = -sigma*ax + sigma*ay;
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k3y = rho*ax - ay - ax*az;
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k3z = -beta*az + ax*ay;
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ax = xi + h*k3x; ay = yi + h*k3y; az = zi + h*k3z;
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k4x = -sigma*ax + sigma*ay;
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k4y = rho*ax - ay - ax*az;
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k4z = -beta*az + ax*ay;
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t(i+1) = ti + h;
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xs(i+1) = xi + h/6 * (k1x + 2*k2x + 2*k3x + k4x);
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ys(i+1) = yi + h/6 * (k1y + 2*k2y + 2*k3y + k4y);
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zs(i+1) = zi + h/6 * (k1z + 2*k2z + 2*k3z + k4z);
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endfor
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% Print every 10th sample
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for i = 1:10:n+1
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printf("%f,%f,%f,%f\n", t(i), xs(i), ys(i), zs(i));
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endfor
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