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Differential Equations

The system discovered by Rössler is given by the following equations:


$\displaystyle \dot{x}$ $\displaystyle =$ $\displaystyle -y-z$  
       
$\displaystyle \dot{y}$ $\displaystyle =$ $\displaystyle x+ay$  
       
$\displaystyle \dot{z}$ $\displaystyle =$ $\displaystyle b+z(x-c)$  

These equations give us a flow on three dimensions which has two stationary points given by


$\displaystyle x$ $\displaystyle =$ $\displaystyle \frac{c \mp \sqrt{c^2-4ab}}{2}$  
       
$\displaystyle y$ $\displaystyle =$ $\displaystyle \frac{-c \pm \sqrt{c^2-4ab}}{2a}$  
       
$\displaystyle z$ $\displaystyle =$ $\displaystyle \frac{c \mp \sqrt{c^2-4ab}}{2a}$  

assuming that $ c$ is sufficiently large compared to $ a$ and $ b$.


next up previous
Next: Analysis of the Equations Up: rossler Previous: Introduction
Kevin Kesseler 2003-07-24