Higher-order networks capture the interactions among two or more nodes and they are raising increasing interest in the study of brain networks. Here we show that higher-order interactions are responsible for new dynamical processes that cannot be observed in pairwise networks.
We will cover how topology is key to define synchronization of topological signals, i.e. dynamical signal defined not only on nodes but also on links, triangles and higher-dimensional simplices in simplicial complexes. Interesting topological synchronization dictated by the Dirac operator can lead to the spontaneous emergence of a rhythmic phase where the synchronization order parameter displays low frequency oscillations which might shed light on possible topological mechanisms for the emergence of brain rhythms.
We will also reveal how triadic interactions, inspired by the triadic interactions between glia and neurons, can turn percolation into a fully-fledged dynamical process in which nodes can turn on and off intermittently in a periodic fashion or even chaotically leading to period doubling and a route to chaos of the percolation order parameter.
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