  In this paper are presented first results of a theoretical study on the role
of non-monotone interactions in Boolean automata networks. We propose to
analyse the contribution of non-monotony to the diversity and complexity in
their dynamical behaviours according to two axes. The first one consists in
supporting the idea that non-monotony has a peculiar influence on the
sensitivity to synchronism of such networks. It leads us to the second axis
that presents preliminary results and builds an understanding of the dynamical
behaviours, in particular concerning convergence times, of specific
non-monotone Boolean automata networks called XOR circulant networks.
