Lorenz 96 model

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


 * $$\frac{dx_i}{dt} = (x_{i+1}-x_{i-2})x_{i-1} - x_i + F$$

where it is assumed that $$x_{-1}=x_{N-1},x_0=x_N$$ and $$x_{N+1}=x_1$$ and $$N \ge 4$$. Here $$x_i$$ is the state of the system and $$F$$ is a forcing constant. $$F=8$$ is a common value known to cause chaotic behavior.

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