Discontinuous phase transition in a core contact process on complex networks

To understand the effect of generalized infection processes, we suggest and study the core contact process (CCP) on complex networks. In CCP an uninfected node is infected when at least k different infected neighbors of the node select the node for the infection. The healing process is the same as that of the normal CP. It is analytically and numerically shown that discontinuous transitions occur in CCP on random networks and scale-free networks depending on infection rate and initial density of infected nodes. The discontinuous transitions include hybrid transitions with β = 1/2 and β = 1. The asymptotic behavior of the phase boundary related to the initial density is found analytically and numerically. The mapping between CCP with k and static (k+1)-core percolation is supposed from the (k+1)-core structure in the active phase and the hybrid transition with β = 1/2. From these properties of CCP one can see that CCP is one of the dynamical processes for the k-core structure on real networks.