Lorentz system

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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