The explosive dynamics present in on-line social networks, typically represented by flaming phenomena, can have a serious impact on not only the sustainable operation of information networks but also on activities in the real world. In order to counter the flaming phenomenon, it is necessary to understand the mechanism underlying the generation of the flaming phenomena within an engineering framework. This paper discusses a new model of the generating mechanism of the flaming phenomena. Our previous study has shown that the cause of flaming phenomena can, by reference to an oscillation model on networks, be understood complex eigenvalues of the matrix formed to describe oscillating phenomena. In this paper, we show that the flaming phenomena can occur due to coupling between degenerated oscillation modes even if all the eigenvalues are real numbers. In addition, we investigate the generation process of flaming phenomena with respect to the initial phases of the degenerated oscillation modes.