The percolation process via a sinusoidal probability modulation

How clusters are aggregated have great effect on the function and dynamic of complex network. In this paper, we introduce a percolation transition model which can be described with clusters aggregated probability P(C
i
) ∼ sin(αC
i
/C
max
), where C
i
is the size of the cluster, C
max
is the size of the largest cluster and α is disturbance parameter. In this article we introduce continuous, weakly and strongly discontinuous percolation transition underlying different α respectively and reveal the strongly impact of clusters' aggregated probability. By means of numerical simulation, we find that the critical point t
c
shows periodic variation with increasing α. Besides, we realize that the largest gap is macroscopic when α >10.9π and the distribution of the cluster size at critical point meets the power laws which is the main feature of explosive percolation.