  In the era of the rapid development of the Internet, the threshold for
information spreading has become lower. Most of the time, rumors, as a special
kind of information, are harmful to society. And once the rumor appears, the
truth will follow. Considering that the rumor and truth compete with each other
like light and darkness in reality, in this paper, we study a rumor spreading
model in the homogeneous network called 2SIH2R, in which there are both
spreader1(people who spread the rumor) and spreader2(people who spread the
truth). In this model, we introduced discernible mechanism and confrontation
mechanism to quantify the level of people's cognitive abilities and the
competition between the rumor and truth. By mean-field equations, steady-state
analysis and numerical simulations in a generated network which is closed and
homogeneous, some significant results can be given: the higher discernible rate
of the rumor, the smaller influence of the rumor; the stronger confrontation
degree of the rumor, the smaller influence of the rumor; the large average
degree of the network, the greater influence of the rumor but the shorter
duration. The model and simulation results provide a quantitative reference for
revealing and controlling the spread of the rumor.
