### Network-network interaction in neuronal systems – how topological characteristics transfer between complex networks

Early Stage Researcher: Nicolás Deschle

Principle Investigators: Andreas Daffertshofer, Bob van Dijk (Amsterdam, VUA – major institution), Björn Schelter (Aberdeen, UABDN – partner institution)

Oscillatory activity can synchronize distant neural ensembles and by this transfer information. The spatial organization of non-local synchronization typically yields complex, so-called small-world or scale-free networks on a functional level. The sparseness of such networks improves their synchronizability* ^{1}* and hence affects the accompanying information transfer. In general, there is strong support that a network perspective on the brain is required for a general understanding of higher brain functioning

*. While switches between frequency bands entail briefly coexisting oscillations, long-lasting coexistence of oscillatory activity is frequently observed in empirical data. Whenever*

^{2,3}*distinct frequency bands coexist*, then the complex, functional networks accompanying these different oscillatory regimes will also co-exist. This raises a question concerning how the networks, and hence the oscillations, interact. Two hypotheses will be tested:

- Not only will local units with distinct frequencies interact, but also entire oscillatory networks will influence each other.
- The small-world character of one network influences that of another network if properly coupled. That is, network properties of one network transfer to that in another e.g., the type of clustering or the randomness is adopted.

We will simulate connected networks of oscillators and test for the interplay between network topologies on the synchronizability of the nodes-defining oscillators using pulse-coupled oscillators (based on leaky integrate-and-fire neurons), neural mass models, and Kuramoto phase oscillators. We will also implement more realistic neural models as soon as the numerical approach for the simpler models is validated. Next, two or more of these networks will be combined in analogy to inhomogeneous or bimodal Kuramoto networks with firing rate or spike-time dependent connectivity. As final step toward biologically sound networks, the connectivity may include finite time delays which compounds the mathematical difficulty and the numerical challenge.

References:

- Barahona, M. & Pecora, L. M. Synchronization in small-world systems.
*Phys Rev Lett***89**, 054101 (2002). - Le Van Quyen, M. Disentangling the dynamic core: a research program for a neurodynamics at
the large-scale.
*Biol Res***36**, 67-88 (2003). - Varela, F., Lachaux, J. P., Rodriguez, E. & Martinerie, J. The brainweb: phase synchronization and
large-scale integration.
*Nat Rev Neurosci***2**, 229-239 (2001).