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The physics of higher-order interactions in complex systems
Federico Battiston, Enrico Amico, Alain Barrat, Ginestra Bianconi, Guilherme Ferraz de Arruda, Benedetta Franceschiello, Iacopo Iacopini, Sonia Kéfi, Vito Latora, Yamir Moreno, Micah M. Murray, Tiago P. Peixoto, Francesco Vaccarino, Giovanni Petri
TL;DR
The paper examines how higher-order interactions extend pairwise network models and reviews their dynamical consequences. It finds that nonlinear higher-order interactions can generate discontinuous transitions, bistability, and hysteresis, while a general proof remains open.
Problem
Pairwise network models struggle to represent explosive transitions observed in systems with higher-order interactions.
Method
The paper synthesizes evidence on higher-order dynamical processes and identifies challenges in modelling, evolving, and reconstructing higher-order structures.
Results
Higher-order interactions can induce discontinuous transitions, bistability, and hysteresis in spreading and oscillator systems.
Takeaways & Limitations
Tuning the relative strength of higher-order and pairwise interactions can change dynamical transitions from continuous to discontinuous.
Takeaways & Limitations
A rigorous and general proof that nonlinear higher-order interactions generically produce abrupt transitions is still lacking.
Abstract
from arXiv · showhide
Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems.
A general pathway to explosive transitions.
Higher-order interactions provide a general route to explosive, discontinuous transitions that are difficult to obtain in pairwise networks. Across contagion and oscillator dynamics, tuning the relative strength of higher-order versus pairwise interactions can generate bistability and change continuous transitions into discontinuous ones.
- A general pathway to explosive transitions.: Higher-order interactions offer a framework in which explosive phenomena emerge, overcoming their difficulty in systems restricted to pairwise interactions.Pairwise-network models typically require artificial elements or rules to produce abrupt order-parameter jumps.
- A general pathway to explosive transitions.: In social contagion on simplicial complexes, increasing the relative weight of higher-order interactions produces a discontinuous transition from healthy to endemic states.Three-body interactions alone can create a bistable region in which endemic and non-endemic states coexist.
- A general pathway to explosive transitions.: Explosive transitions also occur in coupled-oscillator systems when interactions are generalized to include higher-order effects.The node state is influenced by a non-linear combination of several other nodes’ states.
- A general pathway to explosive transitions.: In both contagion and oscillator models, tuning the relative importance of higher-order and pairwise interactions changes the transition from continuous to discontinuous.The shared mechanism is the influence of higher-order interactions through non-linear combinations of multiple node states.