In this post, I'll focus on the Lorenz DE's
These have, for various parameters values, chaotic solutions with interesting trajectory paths often shown:
|A trajectory for the standard Lorenz parameters σ=10, β=8/3, ρ=28. Often displayed without mentioning that specific parameters are required.||An attractor (due to Anders Sandberg, Oxford) parameters not specified but seems close to standard.|
The general idea is that you can compare the effect of changing start points, with comparison red/blue trajectories, and also see the very great range of different attractors that result when the parameters are changed, However, the changes are continuous. What I'd like to get to eventually (future post) is a possible relation between an average of trajectories and the attractor. That would help understand how GCM runs can be averaged to get a climate evolution.