Analysis of non-linear automata with delay 2 over a finite ring

For invertible one-dimensional automata with delay 2 over the ring $\mathbf Z_{p^k}=(\mathbb Z_{p^k},\oplus,\circ)$, the structure of the transition graph is investigated, the sets of equivalent states are characterized, the problems of the parametric identification and of the initial state identification are solved, the sets of fixed points of mappings realized by initial automata are characterized.