Attainability and connectedness in an automata network with a general state switching rule (Q1811515)

The present paper refers to networks with finitely many elements and deals with the most general case: block-sequential iterations with delays. One assumes that the network elements are clustered into blocks, and that inside each block, the states of these elements are switched synchronously. Between the blocks, the state switching is performed sequentially according to some given order. In addition one assumes that the synchronous switching of the elements states inside a given block is performed as a function of the current state of all the network elements and of their previous states. The dynamics of these automata networks is analyzed by using Lyapunov vector functions. Attainability and connectedness criteria are stated.