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arXiv · 2108.08190

Higher-order interactions improve optimal collective dynamics on networks

Per Sebastian Skardal·Lluís Arola-Fernández·Dane Taylor·Alex Arenas
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Abstract

Collective behavior plays a key role in the function of a wide range of physical, biological, and neurological systems where empirical evidence has recently uncovered the prevalence of higher-order interactions, i.e., structures that represent interactions between more than just two individual units, in complex network structures. Here, we study the optimization of collective behavior in networks with higher-order interactions encoded in clique complexes. Our approach involves adapting the Synchrony Alignment Function framework to a new composite Laplacian matrix that encodes multi-order interactions including, e.g., both dyadic and triadic couplings. We show that as higher-order coupling interactions are equitably strengthened, so that overall coupling is conserved, the optimal collective behavior improves. We find that this phenomenon stems from the broadening of a composite Laplacian's eigenvalue spectrum, which improves the optimal collective behavior and widens the range of possible behaviors. Moreover, we find in constrained optimization scenarios that a nontrivial, ideal balance between the relative strengths of pair-wise and higher-order interactions leads to the strongest collective behavior supported by a network. This work provides insight into how systems balance interactions of different types to optimize or broaden their dynamical range of behavior, especially for self-regulating systems like the brain.

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Per Sebastian Skardal, Lluís Arola-Fernández, Dane Taylor, Alex Arenas. 2021-08-18. Higher-order interactions improve optimal collective dynamics on networks. https://doi.org/10.1103/physrevresearch.3.043193

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