Higher-order interactions can better optimize network synchronization
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...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-12-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.043193 |
| _version_ | 1797210872487084032 |
|---|---|
| author | Per Sebastian Skardal Lluís Arola-Fernández Dane Taylor Alex Arenas |
| author_facet | Per Sebastian Skardal Lluís Arola-Fernández Dane Taylor Alex Arenas |
| author_sort | Per Sebastian Skardal |
| collection | DOAJ |
| description | 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 composite Laplacian matrix that encodes multiorder 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 pairwise 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. |
| first_indexed | 2024-04-24T10:17:30Z |
| format | Article |
| id | doaj.art-9d37a582a78d49f7b34380a4051ffd9b |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:17:30Z |
| publishDate | 2021-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-9d37a582a78d49f7b34380a4051ffd9b2024-04-12T17:16:32ZengAmerican Physical SocietyPhysical Review Research2643-15642021-12-013404319310.1103/PhysRevResearch.3.043193Higher-order interactions can better optimize network synchronizationPer Sebastian SkardalLluís Arola-FernándezDane TaylorAlex ArenasCollective 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 composite Laplacian matrix that encodes multiorder 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 pairwise 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.http://doi.org/10.1103/PhysRevResearch.3.043193 |
| spellingShingle | Per Sebastian Skardal Lluís Arola-Fernández Dane Taylor Alex Arenas Higher-order interactions can better optimize network synchronization Physical Review Research |
| title | Higher-order interactions can better optimize network synchronization |
| title_full | Higher-order interactions can better optimize network synchronization |
| title_fullStr | Higher-order interactions can better optimize network synchronization |
| title_full_unstemmed | Higher-order interactions can better optimize network synchronization |
| title_short | Higher-order interactions can better optimize network synchronization |
| title_sort | higher order interactions can better optimize network synchronization |
| url | http://doi.org/10.1103/PhysRevResearch.3.043193 |
| work_keys_str_mv | AT persebastianskardal higherorderinteractionscanbetteroptimizenetworksynchronization AT lluisarolafernandez higherorderinteractionscanbetteroptimizenetworksynchronization AT danetaylor higherorderinteractionscanbetteroptimizenetworksynchronization AT alexarenas higherorderinteractionscanbetteroptimizenetworksynchronization |