COMPETING CONTACT PROCESSES ON HOMOGENEOUS NETWORKS WITH TUNABLE CLUSTERIZATION

Marcin Rybak and Krzysztof Kułakowski ()
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Marcin Rybak: Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland
Krzysztof Kułakowski: Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland

International Journal of Modern Physics C (IJMPC), 2013, vol. 24, issue 03, 1-13

Abstract: We investigate two homogeneous networks: the Watts–Strogatz network with mean degree⟨k⟩ = 4and the Erdös–Rényi network with⟨k⟩ = 10. In both kinds of networks, the clustering coefficientCis a tunable control parameter. The network is an area of two competing contact processes, where nodes can be in two states, S or D. A node S becomes D with probability 1 if at least two its mutually linked neighbors are D. A node D becomes S with a given probabilitypif at least one of its neighbors is S. The competition between the processes is described by a phase diagram, where the critical probabilitypcdepends on the clustering coefficientC. Forp > pcthe rate of state S increases in time, seemingly to dominate in the whole system. Belowpc, the majority of nodes is in the D-state. The numerical results indicate that for the Watts–Strogatz network the D-process is activated at the finite value of the clustering coefficientC, close to 0.3. On the contrary, for the Erdös–Rényi network the transition is observed at the whole investigated range ofC.

Keywords: Contact processes; Monte Carlo simulations; homogeneous networks; 07.05.Tp; 64.60.aq; 89.65.Ef (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183113500125

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