An adaptive voter model on simplicial complexes

Abstract

Collective decision making processes lie at the heart of many social, political and economic challenges. The classical voter model is a well-established conceptual model to study such processes. In this work, we define a new form of adaptive (or co-evolutionary) voter model posed on a simplicial complex, i.e., on a certain class of hypernetworks/hypergraphs. We use the persuasion rule along edges of the classical voter model and the recently studied re-wiring rule of edges towards like-minded nodes, and introduce a new peer pressure rule applied to three nodes connected via a 2-simplex. This simplicial adaptive voter model is studied via numerical simulation. We show that adding the effect of peer pressure to an adaptive voter model leaves its fragmentation transition, i.e., the transition upon varying the re-wiring rate from a single majority state into to a fragmented state of two different opinion subgraphs, intact. Yet, above and below the fragmentation transition, we observe that the peer pressure has substantial quantitative effects. It accelerates the transition to a single-opinion state below the transition and also speeds up the system dynamics towards fragmentation above the transition. Furthermore, we quantify that there is a multiscale hierarchy in the model leading to the depletion of 2-simplices, before the depletion of active edges. This leads to the conjecture that many other dynamic network models on simplicial complexes may show a similar behaviour with respect to the sequential evolution of simplicies of different dimensions.

10 pages, 6 figures

References in corpus (26)

• Epidemic dynamics on an adaptive network
• Co-evolution of strategy and structure in complex networks with dynamical linking
• Voter Model on Heterogeneous Graphs
• Simplicial Closure and higher-order link prediction
• Minority Opinion Spreading in Random Geometry
• Dynamics of Majority Rule
• Voter Models on Heterogeneous Networks
• Critical Coarsening without Surface Tension: the Voter Universality Class
• Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution
• Generic Absorbing Transition in Coevolution Dynamics
• Consensus formation on adaptive networks
• Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics
• Incomplete ordering of the voter model on small-world networks
• Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model
• Binary-state dynamics on complex networks: pair approximation and beyond
• Analytical Solution of the Voter Model on Disordered Networks
• Who's talking first? Consensus or lack thereof in coevolving opinion formation models
• Moment Closure - A Brief Review
• Triadic closure dynamics drives scaling-laws in social multiplex networks
• Analytical calculation of fragmentation transitions in adaptive networks
• Adaptive-network models of swarm dynamics
• Early fragmentation in the adaptive voter model on directed networks
• Early warning signs for saddle-escape transitions in complex networks
• Zealotry Effects on Opinion Dynamics in the Adaptive Voter Model
• Consensus time and conformity in the adaptive voter model
• Network topology near criticality in adaptive epidemics

Cited by in corpus (31)

• Networks beyond pairwise interactions: structure and dynamics
• Dynamics on higher-order networks: A review
• What are higher-order networks?
• The effect of heterogeneity on hypergraph contagion models
• Coupled Dynamics on Hypergraphs: Master Stability of Steady States and Synchronization
• Desynchronization transitions in adaptive networks
• Group interactions modulate critical mass dynamics in social convention
• Perspectives on adaptive dynamical systems
• Heterogeneous nucleation in finite size adaptive dynamical networks
• Higher-Order Components Dictate Higher-Order Contagion Dynamics in Hypergraphs
• Consensus on simplicial complexes, or: The nonlinear simplicial Laplacian
• Dynamics of Majority Rule on Hypergraphs
• Stochastic epidemic model on a simplicial complex
• Stability analysis of multiplayer games on adaptive simplicial complexes
• Collective dynamics on higher-order networks
• Emergence of complex structures from nonlinear interactions and noise in coevolving networks
• Coupled Hypergraph Maps and Chaotic Cluster Synchronization
• Polyadic Opinion Formation: The Adaptive Voter Model on a Hypergraph
• Recurrent chaotic clustering and slow chaos in adaptive networks
• Hypergraphon Mean Field Games
• Group adaptation drives opinion dynamics in higher-order networks
• Adaptive behaviors neutralize bistable explosive transitions in higher-order contagion
• Coevolutionary Dynamics of Group Interactions: Coevolving Nonlinear Voter Models
• On the convergence of nonlinear averaging dynamics with three-body interactions on hypergraphs
• The topology of higher-order complexes associated with brain-function hubs in human connectomes
• Consensus from group interactions: An adaptive voter model on hypergraphs
• Aging in coevolving voter models
• Edge corona product as an approach to modeling complex simplical networks
• Phase transitions for polyadic epidemic and voter models with multiscale groups
• Emergence of solitary and chimera states in adaptive pendulum networks under diverse learning rules
• Construction of simplicial complexes with prescribed degree-size sequences