Аннотация
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 \$łambda\$ and infected individuals recover
(\$1 0\$) at rate 1. In the QCP, a combination of two 1's is
required to effect a \$0 1\$ change. We extend the study of the
QCP, which so far has been limited to lattices, to complex networks.
as a model for the change in a population through sexual reproduction
and death. We define two versions of the QCP -- vertex centered (VQCP) and
edge centered (EQCP) with birth events \$1-0-1 1-1-1\$ and \$1-1-0
1-1-1\$ respectively, where `\$-\$' represents an edge. We
investigate the effects of network topology by considering the QCP on random
regular, Erd\Hos-Rényi 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 Erd\Hos-Rényi 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.
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