Lorenz 96 model

The Lorenz 96 model is a dynamical system formulated by Edward Lorenz in 1996. It is defined as follows. For ${\displaystyle i=1,...,N}$:

${\displaystyle {\frac {dx_{i}}{dt}}=(x_{i+1}-x_{i-2})x_{i-1}-x_{i}+F}$

where it is assumed that ${\displaystyle x_{-1}=x_{N-1},x_{0}=x_{N}}$ and ${\displaystyle x_{N+1}=x_{1}}$ and ${\displaystyle N\geq 4}$. Here ${\displaystyle x_{i}}$ is the state of the system and ${\displaystyle F}$ is a forcing constant. ${\displaystyle F=8}$ is a common value known to cause chaotic behavior.

It is commonly used as a model problem in data assimilation.