Two types of nonlinear automata over a finite ring

The structure of a class of automata is analyzed. These automata are analogs of symmetric chaotic dynamical systems over a finite ring, namely, the Guckenheimer–Holmes cycle and free-running systems. Problems of parametric identification and identification of initial states are solved, and a set of fixed points of automaton mappings is characterized. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 57–68, July–August 2009.