  The understanding of Boolean automata networks dynamics takes an important
place in various domains of computer science such as computability, complexity
and discrete dynamical systems. In this paper, we make a step further in this
understanding by focusing on their cycles, whose necessity in networks is known
as the brick of their complexity. We present new results that provide a
characterisation of the transient and asymptotic dynamics, i.e. of the
computational abilities, of asynchronous Boolean automata networks composed of
two cycles that intersect at one automaton, the so-called double-cycles. To do
so, we introduce an efficient formalism inspired by algorithms to define long
sequences of updates, that allows a better description of their dynamics than
previous works in this area.
