Effects of network topology are studied in a system of cellular automata driven by a totalistic rule. In particular, propagation of a signal is considered in the directed network obtained from a flat (square) lattice by adding directed connections. The model is motivated by features found in human neural system. Cooperation between local dynamics and network organization results in fast stabilization of the system. Simple model of neural pyramidal cell is proposed to stabilize the automata in the oscillating firing patterns form.

PACS numbers: 05.70.Ln, 87.17.Aa, 87.18.Sn, 87.19.La