Lorenz-95

Lorenz-95 is a dynamical system formulated by Edward Lorenz in 1995^[1] . It is defined as follows:

$\frac{dx_i}{dt} = -x_{i-2}x_{i-1} %2B x_{i-1}x_{i%2B1} - x_i %2B F$

where $x_i$ 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^[2]

References

^ Lorenz, Edward (1995). "Predictability – A problem partly solved". Seminar on Predictability, Vol. I, ECMWF. http://eapsweb.mit.edu/research/Lorenz/Predicability_a_Problem_2006.pdf.
^ Leutbecher, Martin. "A data assimilation tutorial based on the Lorenz-95 system". http://www.ecmwf.int/newsevents/training/meteorological_presentations/pdf/DA/ToyModel_notes.pdf.