Ginestra Bianconi

School of Mathematical Sciences of Queen Mary University of London
United Kingdom

Higher-order and topological synchronization

Abstract

Higher-order networks [1] describe the many-body 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 higher-order networks. In this talk we will show that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics including synchronization depends on simplicial network topology. We will show that higher-order synchronization describing the dynamics of topological signals defined on link, triangles and higher-dimensional simplices is explosive [2-4] and we will show that this rich dynamics can shade new light on the topological mechanisms that could lead to brain rhythms.

References

  1. G. Bianconi, Higher-order networks: An introduction to simplicial complexes (Cambridge University Press, 2021).

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

  3. Ghorbanchian, R., Restrepo, J.G., Torres, J.J. and Bianconi, G., 2021. Higher-order simplicial synchronization of coupled topological signals. Communications Physics, 4(1), pp.1-13.

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

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