Table 1 Description of the notation in Eq. 1

Number of automata in the network

Number of states, where the state space of each automaton is {0,1,⋯,K−1}

Number of synchronizing events and an index of each event, respectively

Local transition rate matrix (normalized) of the automaton i

Effect matrix corresponding to the r^th synchronizing event acting on the automaton i

Normalizing matrix needed for the tensor product of M_r,i to constitute a transition rate matrix