(3/3)
- Linearizing around the nearest fixed point captures roughly the true velocity...
- ...but linearizing around the second-nearest is only slightly worse.
-> Fixed points collectively attract and lur the dynamics

For detailed analytical and numerical analysis check doi.org/10.1103/Phys...

(2/3) Key findings:
- The number of fixed points is exponential in number of neurons
- Fixed points concentrate on a shell withing the shell where the dynamics concentrates -> radial separation
- Yet, dynamics and fixed points live near the same low-dimensional manifold

(1/3) How to analyse a dynamical system? Find its fixed points, study their properties!

How to analyse a *high-dimensional* dynamical system? Find its fixed points, study their properties!

We do that for a chaotic neural network! finally published: doi.org/10.1103/Phys...