Math @ Duke

Publications [#243423] of Richard T. Durrett
Papers Published
 Varghese, C; Durrett, R, Phase transitions in the quadratic contact process on complex networks,
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 87 no. 6
(2013),
pp. paper 062819, ISSN 15393755 [doi]
(last updated on 2018/08/20)
Abstract: The quadratic contact process (QCP) is a natural extension of the wellstudied linear contact process where infected (1) individuals infect susceptible (0) neighbors at rate λ and infected individuals recover (1ï·0) at rate 1. In the QCP, a combination of two 1's is required to effect a 0ï·1 change. We extend the study of the QCP, which so far has been limited to lattices, to complex networks. We define two versions of the QCP: vertexcentered (VQCP) and edgecentered (EQCP) with birth events 101ï·111 and 110ï·111, respectively, where "" represents an edge. We investigate the effects of network topology by considering the QCP on random regular, ErdosRényi, and powerlaw random graphs. We perform meanfield calculations as well as simulations to find the steadystate fraction of occupied vertices as a function of the birth rate. We find that on the random regular and ErdosRényi graphs, there is a discontinuous phase transition with a region of bistability, whereas on the heavytailed powerlaw graph, the transition is continuous. The critical birth rate is found to be positive in the former but zero in the latter. © 2013 American Physical Society.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

