Phase transitions in the quadratic contact process on complex networks
Chris Varghese and Rick Durrett
Abstract.
The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where infected (1) individuals infect susceptible (0)
neighbors at rate λ and infected individuals recover at rate 1. In the QCP, a combination of two 1's is required to couse a birth. 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 -- vertex centered (VQCP) and edge centered (EQCP)
with birth events 1-0-1 to 1-1-1 and 1-1-0 to 1-1-1 respectively, where the dashes represents an edges. We investigate the effects of network topology by considering the QCP on random regular, Erdos-Renyi
and power law random graphs. We perform mean field calculations as well as simulations to find the steady state fraction of occupied vertices as a function of the birth rate. We find that on the random regular
and Erdos-Renyi graphs, there is a discontinuous phase transition with a region of bistability, whereas on the heavy tailed power law graph, the transition is continuous. The critical birth rate is found to be positive
in the former but zero in the latter.
Preprint Phys. Rev E 87 (20130, paper 062819
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