  Boolean automata networks (BANs) are a well established model for biological
regulation systems such as neural networks or genetic networks. Studies on the
dynamics of BANs, whether it is synchronous or asynchronous, have mainly
focused on monotonic networks, where fundamental questions on the links
relating their static and dynamical properties have been raised and addressed.
This paper explores analogous questions on asynchronous non-monotonic networks,
xor-BANs, that are BANs where all the local transition functions are
xor-functions. Using algorithmic tools, we give a general characterisation of
the asynchronous transition graphs for most of the cactus xor-BANs and strongly
connected xor-BANs. As an illustration of the results, we provide a complete
description of the asynchronous dynamics of two particular classes of xor-BAN,
namely xor-Flowers and xor-Cycle Chains. This work also leads to new
bisimulation equivalences specific to xor-BANs.
