Titlebook: Higher-Order Systems; Federico Battiston,Giovanni Petri Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license

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Random Simplicial Complexes: Models and Phenomena,o cover all existing models, but try to focus on those for which many important results have been recently established rigorously in mathematics, especially in the context of algebraic topology. In application to real-world systems, the reviewed models are typically used as null models, so that we t

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Pattern Formation on Hypergraphs,processes can be ideally traced back to the proposed scheme. We shall here solely elaborate on the conditions that seed the spontaneous emergence of patterns, spatially heterogeneous solutions resulting from the many-body interaction between fundamental units. In particular we will focus, on two rel

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From Symmetric Networks to Heteroclinic Dynamics and Chaos in Coupled Phase Oscillators with Higherase oscillators in networks with fully symmetric coupling. For systems near Hopf bifurcation the lowest order (pairwise) interactions correspond to the system of Kuramoto and Sakaguchi. At next asymptotic order one must generically include higher-order interactions of up to four oscillators. We disc

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,Explosive Synchronization and Multistability in Large Systems of Kuramoto Oscillators with Higher-Oof nonlinear collective behavior. However, recent evidence suggests that in such phase-reduced systems, interactions beyond the typical pair-wise angle differences need to be considered to develop a full picture of the dynamics. In particular, ., namely non-additive, nonlinear interactions that take

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