Diffusion on hierarchical systems of weakly-coupled networks
arXiv:1303.2650 · doi:10.1016/j.physa.2018.08.078
Abstract
We analyse diffusion dynamics on weakly-coupled networks (interconnected networks) by means of separation of time scales. Using an adiabatic approximation we reduced the system dynamics to a Markov chain with aggregated variables and derived a transport equation that is analogous to Fick's First Law and includes a driving force. Entropy production is a sum of microscopic entropy transport, which results from the particle's migration between networks of different topologies and macroscopic entropy production of the Markov chain. Equilibrium particles partition between different sub-networks depends only on internal sub-network parameters. Our framework, confirmed by numerical simulations, is also useful for considering diffusion in nested systems corresponding to hierarchical networks with several different time scales thus it can serve to uncover hidden hierarchy levels from observations of diffusion processes.
13 pages, 7 figures
References in corpus (24)
- Uncovering the overlapping community structure of complex networks in nature and society
- Maps of random walks on complex networks reveal community structure
- Epidemic processes in complex networks
- Multilayer Networks
- Hierarchical structure and the prediction of missing links in networks
- Community detection in networks: A user guide
- Diffusion dynamics on multiplex networks
- Extracting the hierarchical organization of complex systems
- Locating the Source of Diffusion in Large-Scale Networks
- Multilevel compression of random walks on networks reveals hierarchical organization in large integrated systems
- Optimal network modularity for information diffusion
- Multiplex PageRank
- Reconstructing propagation networks with natural diversity and identifying hidden sources
- Entropy Rate of Diffusion Processes on Complex Networks
- Scale-free network growth by ranking
- Percolation of a general network of networks
- Maximal-entropy random walks in complex networks with limited information
- Pair approximation for the q-voter model with independence on complex networks
- Phase transitions in the q-voter model with noise on a duplex clique
- Conformism-driven phases of opinion formation on heterogeneous networks: the q-voter model case
- Characterization of the Nonequilibrium Steady State of a Heterogeneous Nonlinear -Voter Model with Zealotry
- Ising model on two connected Barabasi-Albert networks
- Origin of the hub spectral dimension in scale-free networks
- Random Walks on Complex Networks