Reaction-diffusion equation on a graph and phase transition on bistable media

Recently, fast and furious changes come to existence in various fields. In this paper, we identify a state before a change and the other state after the change as two stable stationary states of bistable media, and identify the change as the phase transition between two stable stationary states. The fast phase transition propagating in the media is called a trigger wave, which we identify the above fast and furious changes observed in various fields. First, we consider when and how these trigger wave occur in the continuous bistable media, then we prospect the bistable media on graph structure.