$$\phi_X^{n+1} = \phi_X^n + \Delta t~(-\sigma X~+~\sigma Y)$$
$$\phi_Y^{n+1} = \phi_Y^n + \Delta t~(-XZ~+rZ-~Y)$$
$$\phi_Z^{n+1} = \phi_Z^n + \Delta t~(XY~-~bZ)$$
$$\frac{d\vec{x}}{dt}=f_D(\vec{x}) ~ + ~ f_K(\vec{x})$$
![Example](/mammatus95/Lorenz/raw/main/example/lorenz_rk.png)
![Example](/mammatus95/Lorenz/raw/main/example/lorenz_euler.png)
$$x_{n+1} = y_n +1 - a x^2_n$$
$$y_{n+1} ,=, \beta x_n$$
$\alpha$=1.4
$\beta$=0.3
$$X=1-\alpha X^2 + bX$$
$$\dot{x} ,=, -y ,-, z$$
$$\dot{y} ,=, x ,+, \alpha y$$
$$\dot{z} ,=, \beta ,+, z(x,-,c)$$
$\alpha$=$\beta$=0.2
c=5.7