Reaction|[ndash]|diffusion processes and metapopulation models in heterogeneous|[nbsp]|networks

Vittoria Colizza; Romualdo Pastor-Satorras; Alessandro Vespignani

doi:doi:10.1038/nphys560

Nature Physics 3, 276 - 282 (2007)
Published online: 4 March 2007 | doi:10.1038/nphys560

Subject Category: Statistical physics, thermodynamics and nonlinear dynamics

Reaction–diffusion processes and metapopulation models in heterogeneous networks

Vittoria Colizza^1,², Romualdo Pastor-Satorras³ & Alessandro Vespignani^1,²

Dynamical reaction–diffusion processes and metapopulation models are standard modelling approaches for a wide array of phenomena in which local quantities—such as density, potentials and particles—diffuse and interact according to the physical laws. Here, we study the behaviour of the basic reaction–diffusion process (given by the reaction steps B right arrow A and B+A2B) 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 metapopulation and agent-based models that include the complex features of real-world networks.

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Complex Networks Lagrange Laboratory, Institute for Scientific Interchange (ISI), Torino 10133, Italy
School of Informatics and Department of Physics, Indiana University, Bloomington 47406 Indiana, USA
Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain

Correspondence to: Vittoria Colizza^1,² e-mail: vcolizza@indiana.edu

Correspondence to: Alessandro Vespignani^1,² e-mail: alexv@indiana.edu