Ginestra Bianconi
School of Mathematical Sciences of Queen Mary University of London
United Kingdom
Higherorder and topological synchronization
Abstract
Higherorder networks [1] describe the manybody interactions of a large variety of complex systems, ranging from the brain to scientific collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higherorder networks. In this talk we will show that simplicial complexes provide a very general mathematical framework to reveal how higherorder dynamics including synchronization depends on simplicial network topology. We will show that higherorder synchronization describing the dynamics of topological signals defined on link, triangles and higherdimensional simplices is explosive [24] and we will show that this rich dynamics can shade new light on the topological mechanisms that could lead to brain rhythms.
References

G. Bianconi, Higherorder networks: An introduction to simplicial complexes (Cambridge University Press, 2021).

Millán, A.P., Torres, J.J. and Bianconi, G., 2020. Explosive higherorder Kuramoto dynamics on simplicial complexes. Physical Review Letters, 124(21), p.218301.

Ghorbanchian, R., Restrepo, J.G., Torres, J.J. and Bianconi, G., 2021. Higherorder simplicial synchronization of coupled topological signals. Communications Physics, 4(1), pp.113.

Calmon, L., Restrepo, J.G., Torres, J.J. and Bianconi, G., 2021. Topological synchronization: explosive transition and rhythmic phase. arXiv preprint arXiv:2107.05107.