Asynchronous dynamics of boolean automata double-cycles

Abstract : Because interaction networks occupy more and more space in our current life (social networks) and in our understanding of living systems(biological regulation networks), it seems necessary to develop the knowledge regarding them. By using Boolean automata networks as models of interaction networks, we present new results about the influence of cycles on their dynamics. Cycles in the architecture of boolean networks are known to be the primary engine of dynamical complexity. As a first particular case, we focus on cycle intersections and provide a characterisation of the dynamics of asynchronous Boolean automata networks composed of two cycles that intersect at one automaton. To do so, we introduce an efficient formalism inspired by algorithms to define long sequences of updates, which allows a more efficient description of their dynamics.