Symmetry Breaking Dynamic States and Multi-stability in Complex Neural Networks




Greater Copenhagen area

Background. Brain dynamics are a product of millions of interacting units and difficult to understand. To tackle this problem we use simplified models to describe qualitative features, i.e., we use so-called coarse grained models. To capture the dynamics of large groups of densely connected neurons (neural masses). Neural masses represent nodes on a weighted graph (Figure panel (a)), and their neural activity is described by a phase θj (t). While large-scale synchronization in the brain is pathological (such as epileptic seizure), normal brain activity exhibits non-uniform synchronization patterns which keep changing in time, thus allowing the brain to maintain function and to perform computations.

Project description. It is well known that non-uniform synchronization can be exhibited in oscillator networks with non-uniform coupling strength. Such systems exhibit multi-stability, i.e. the system can be dynamically switched from one state to an other, thus lending function to a neural network. Imminent questions are therefore: what are the number of multi-stable non-uniform synchronization patterns on a given (arbitrary) weighted network? And what are minimal symmetry conditions imposed on a network for multi-stability to occur?

Possible project goals:
1. Numerical simulations of experimentally measured neural networks, probing multi-stability via MC sampling of initial conditions
2. Determine solution space / attractors for phase oscillator models and/or reduced mean-field dynamical equations
3. Comparison to more complex/realistic neural models
4. Which ones of the attractors are forced by the structure and symmetry properties of the system?
5. ...
Possible methods: Numerical simulation, network/graph theory, bifurcation theory, dimensional reduction, (concepts of group & representation theory*).

In collaboration with

Christian Bick

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