Lorenz

Compile

gcc -o lorenz lorenz.c

Lorenz attractor

$$\phi_X^{n+1} = \phi_X^n + \Delta t~(-\sigma X~+~\sigma Y)$$

$$\phi_Y^{n+1} = \phi_Y^n + \Delta t~(-XZ~+rZ-~Y)$$

$$\phi_Z^{n+1} = \phi_Z^n + \Delta t~(XY~-~bZ)$$

$$\frac{d\vec{x}}{dt}=f_D(\vec{x}) ~ + ~ f_K(\vec{x})$$

Example

henon map

$$x_{n+1} = y_n +1 - a x^2_n$$

$$y_{n+1} ,=, \beta x_n$$

$\alpha$=1.4

$\beta$=0.3

fix points

$$X=1-\alpha X^2 + bX$$

Rössler-Attraktor

$$\dot{x} ,=, -y ,-, z$$

$$\dot{y} ,=, x ,+, \alpha y$$

$$\dot{z} ,=, \beta ,+, z(x,-,c)$$

$\alpha$=$\beta$=0.2 c=5.7