What if the secret to understanding complex systems like the brain, climate, and AI algorithms lies not only in simple pairwise relationships but also in higher-order interactions? A recent study, published in Nature Physics and co-authored by Nordita researcher Hanlin Sun, offers new insights into the interplay between network topology and dynamics in complex systems. Traditional theoretical approaches in network science often rely on the assumption that interactions are dyadic (between pairs of nodes), which limits the analysis of higher-order networks. This study introduces a framework that emphasizes the critical role of higher-order networks, capturing many-body interactions, in shaping the dynamics of complex systems. Specifically, it explores how topology influences dynamics, how dynamics shapes topology, and how both evolve together.
Hanlin Sun comments that the most exciting aspect of this research is its unconventional approach, combining discrete topology and nonlinear dynamics. “This powerful framework allows for a deeper understanding of processes on higher-order networks,” says Sun, “addressing phenomena such as topological synchronization, pattern formation, and triadic percolation. The insights gained could help answer critical questions in many scientific disciplines.”
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