Lorentz system

Download

Flow* Lorentz.model

Model description

The Lorentz system is a simplified model which is developed by Edward Lorenz for atmospheric convection. It is described by a 3-dimensional ODE

      \[   \left\{   \begin{array}{lcl}    \dot{x} & = & \sigma\cdot (y - x) \\    \dot{y} & = & x \cdot (\rho - z) - y \\    \dot{z} & = & x\cdot y - \beta\cdot z   \end{array}   \right.  \]

wherein  \sigma = 10 ,  \rho = \frac{8}{3} ,  \beta = 28 .

Reachability settings

We consider the initial set  x\in [14.999,15.001] ,  y\in [14.999,15.001] ,  z\in [35.999,36.001] .

Results

The following figure shows the  x  y projection of an overapproximation computed by Flow* for the time horizon  [0,6.5] :

Lorentz