Moment-Closure Approximations for Discrete Adaptive Networks
arXiv:1211.0449
Abstract
Moment-closure approximations are an important tool in the analysis of the dynamics on both static and adaptive networks. Here, we provide a broad survey over different approximation schemes by applying each of them to the adaptive voter model. While already the simplest schemes provide reasonable qualitative results, even very complex and sophisticated approximations fail to capture the dynamics quantitatively. We then perform a detailed analysis that identifies the emergence of specific correlations as the reason for the failure of established approaches, before presenting a simple approximation scheme that works best in the parameter range where all other approaches fail. By combining a focused review of published results with new analysis and illustrations, we seek to build up an intuition regarding the situations when existing approaches work, when they fail, and how new approaches can be tailored to specific problems.
22 pages, 14 figures, This is the extended version of the paper, containing the complete derivation of the results
References in corpus (59)
- Emergence of scaling in random networks
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Statistical physics of social dynamics
- Critical phenomena in complex networks
- Epidemic dynamics and endemic states in complex networks
- Epidemic dynamics on an adaptive network
- Co-evolution of strategy and structure in complex networks with dynamical linking
- Voter Model on Heterogeneous Graphs
- Nonequilibrium phase transition in the coevolution of networks and opinions
- Dynamical synapses causing self-organized criticality in neural networks
- Coevolution of dynamical states and interactions in dynamic networks
- A mathematical framework for critical transitions: bifurcations, fast-slow systems and stochastic dynamics
- Voter Models on Heterogeneous Networks
- Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution
- Generic Absorbing Transition in Coevolution Dynamics
- Delays, connection topology, and synchronization of coupled chaotic maps
- Consensus formation on adaptive networks
- Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics
- Fluctuating epidemics on adaptive networks
- Incomplete ordering of the voter model on small-world networks
- High-accuracy approximation of binary-state dynamics on networks
- Adaptive networks: coevolution of disease and topology
- Failure of adaptive self-organized criticality during epileptic seizure attacks
- Conservation laws for the voter model in complex networks
- Analytical Solution of the Voter Model on Disordered Networks
- Who's talking first? Consensus or lack thereof in coevolving opinion formation models
- Evolutionary game dynamics in a growing structured population
- Adaptive synchronization of dynamics on evolving complex networks
- Adaptive self-organization in a realistic neural network model
- Comparison of voter and Glauber ordering dynamics on networks
- Enhanced vaccine control of epidemics in adaptive networks
- Self-organized critical neural networks
- Emergent Hierarchical Structures in Multiadaptive Games
- Coevolution of agents and networks: Opinion spreading and community disconnection
- Solution of voter model dynamics on annealed small-world networks
- Opinion and community formation in coevolving networks
- Dynamics of networking agents competing for high centrality and low degree
- Heterogeneous pair approximation for voter models on networks
- Epidemic threshold and control in a dynamic network
- Quarantine generated phase transition in epidemic spreading
- Time scale competition leading to fragmentation and recombination transitions in the coevolution of network and states
- Analytical calculation of fragmentation transitions in adaptive networks
- Early fragmentation in the adaptive voter model on directed networks
- Consensus formation on coevolving networks: groups' formation and structure
- Anomalous lifetime distributions and topological traps in ordering dynamics
- A homoclinic route to asymptotic full cooperation in adaptive networks and its failure
- Maximum-entropy moment-closure for stochastic systems on networks
- Lack of consensus in social systems
- General coevolution of topology and dynamics in networks
- Fragmentation transitions in multi-state voter models
- Graphical notation reveals topological stability criteria for collective dynamics in complex networks
- Epidemic spreading on preferred degree adaptive networks
- Studies of opinion stability for small dynamic networks with opportunistic agents
- STDP-driven networks and the \emph{C. elegans} neuronal network
- Evolution of network structure by temporal learning
- Instability in a Network Coevolving with a Particle System
- Absence of epidemic thresholds in a growing adaptive network
- Detecting and Describing Dynamic Equilibria in Adaptive Networks