# Lorenz system

## An interactive simulation of a chaotic attractor

created by Hendrik Wernecke

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*summer term 2018*—
The Lorenz system was defined by Lorenz [1] and is very important.

### Simulation

time $t = $0.00

$\rho=$

### Usage

This simulation is damn hard to use. Press the START button and it runs. Press STOP and it stops.### Theory

This is the Lorenz system:
\begin{align}
\dot{x} &= \sigma(y-x)\\
\dot{y} &= x(\rho-z)-y\\
\dot{z} &= xy-\beta z\,.
\end{align}
We use $\beta=8/3$ and $\sigma=10$ and keep $\rho$ as a parameter
The syste has the following

For $r=28$ the Lorenz system is chaotic and then it looks like

**fixed points**\begin{align} \mathbf{v}_\text{o} &= (0,0,0)\\ \mathbf{v}_{1,2} &= \left(\pm\sqrt{\beta(\rho-1)},\pm\sqrt{\beta(\rho-1)},\rho-1\right) \end{align} which are also indicated on the canvas.For $r=28$ the Lorenz system is chaotic and then it looks like

**Figure:** The Lorenz butterfly.

### Code & documentation

Here I want to show some parts of the JavaScript code that I am fond of:- solving the Lorenz ODE by Euler integration

- the core drawing function looks like this

### Acknowledgements, authors & contact

Acknowledgements The author would like to thank everyone.About the authors Hendrik Wernecke is a PhD student in the group of Prof. C. Gros at Goethe University Frankfurt (Main).

Contact For questions, suggestions or comments on this simulation, please contact click to show email

### References & further reading

- [1]
- Deterministic nonperiodic flow., J. Atmos. Sci. 20(2) 1963. :

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