Reaction-diffusion processes and metapopulation models in heterogeneous networks

Abstract

Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the physical laws. Here, we study the behavior of two basic reaction-diffusion processes ($B\to A$ and $A+B\to 2B$) defined on networks with heterogeneous topology and no limit on the nodes' occupation number. We investigate the effect of network topology on the basic properties of the system's phase diagram and find that the network heterogeneity sustains the reaction activity even in the limit of a vanishing density of particles, eventually suppressing the critical point in density driven phase transitions, whereas phase transition and critical points, independent of the particle density, are not altered by topological fluctuations. This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic meta-populations models and agent-based models that include the complex features of real world networks.

22 pages, 4 figures. For related work and info, visit the Cx-Nets webpage at http://cxnets.googlepages.com/. Nature Physics, in press (2007)

References in corpus (16)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Epidemic spreading in scale-free networks
• Assortative mixing in networks
• The architecture of complex weighted networks
• Network robustness and fragility: Percolation on random graphs
• Resilience of the Internet to random breakdowns
• The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles
• Dynamical and correlation properties of the Internet
• The Web of Human Sexual Contacts
• Prediction and predictability of global epidemics: the role of the airline transportation network
• Forecast and Control of Epidemics in a Globalized World
• Generation of uncorrelated random scale-free networks
• Scaling laws for the movement of people between locations in a large city
• Wilson renormalization of a reaction-diffusion process
• Field theory of absorbing phase transitions with a non-diffusive conserved field

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• Contagion dynamics in time-varying metapopulation networks
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• Traveling and pinned fronts in bistable reaction-diffusion systems on network
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• Multiple peaks patterns of epidemic spreading in multi-layer networks
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• Effects of mobility on ordering dynamics
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