The concept of neural masses, an application of mean field theory, is introduced as a possible surrogate for electrophysiological signals in brain simulation. The mathematics of neural mass models and their integration to a coupled network are explained.

Bifurcation analysis is presented as an important technique in the understanding of non-linear systems and as a fundamental method in the design of brain simulations.

Finally, the application of the described mathematics is demonstrated in the exploration of brain stimulation regimes.

## Topics covered in this lesson by Andreas Spiegler

- Mathematical description of neural masses
- Transfer functions in local brain dynamics
- Mathematical implementation of structural connectivity
- The Jansen-Rit model
- Bifurcation analysis
- Equilibrium manifolds
- Dynamics of brain stimulation