000101619 001__ 101619 000101619 005__ 20230519145422.0 000101619 0247_ $$2doi$$a10.1038/s42005-021-00525-3 000101619 0248_ $$2sideral$$a123931 000101619 037__ $$aART-2021-123931 000101619 041__ $$aeng 000101619 100__ $$aFerraz de Arruda, G. 000101619 245__ $$aPhase transitions and stability of dynamical processes on hypergraphs 000101619 260__ $$c2021 000101619 5060_ $$aAccess copy available to the general public$$fUnrestricted 000101619 5203_ $$aHypergraphs naturally represent higher-order interactions, which persistently appear in social interactions, neural networks, and other natural systems. Although their importance is well recognized, a theoretical framework to describe general dynamical processes on hypergraphs is not available yet. In this paper, we derive expressions for the stability of dynamical systems defined on an arbitrary hypergraph. The framework allows us to reveal that, near the fixed point, the relevant structure is a weighted graph-projection of the hypergraph and that it is possible to identify the role of each structural order for a given process. We analytically solve two dynamics of general interest, namely, social contagion and diffusion processes, and show that the stability conditions can be decoupled in structural and dynamical components. Our results show that in social contagion process, only pairwise interactions play a role in the stability of the absorbing state, while for the diffusion dynamics, the order of the interactions plays a differential role. Our work provides a general framework for further exploration of dynamical processes on hypergraphs. 000101619 536__ $$9info:eu-repo/grantAgreement/ES/DGA/ER36-20R$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/FIS2017-87519-P 000101619 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000101619 590__ $$a6.497$$b2021 000101619 592__ $$a2.13$$b2021 000101619 594__ $$a8.2$$b2021 000101619 591__ $$aPHYSICS, MULTIDISCIPLINARY$$b16 / 86 = 0.186$$c2021$$dQ1$$eT1 000101619 593__ $$aPhysics and Astronomy (miscellaneous)$$c2021$$dQ1 000101619 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000101619 700__ $$aTizzani, M. 000101619 700__ $$0(orcid)0000-0002-0895-1893$$aMoreno, Y.$$uUniversidad de Zaragoza 000101619 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000101619 773__ $$g4 (2021), 24 [9 pp]$$tCommunications Physics$$x2399-3650 000101619 8564_ $$s1511500$$uhttps://zaguan.unizar.es/record/101619/files/texto_completo.pdf$$yVersión publicada 000101619 8564_ $$s1180678$$uhttps://zaguan.unizar.es/record/101619/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000101619 909CO $$ooai:zaguan.unizar.es:101619$$particulos$$pdriver 000101619 951__ $$a2023-05-18-14:08:03 000101619 980__ $$aARTICLE