  This paper aims at setting the keystone of a prospective theoretical study on
the role of non-monotone interactions in biological regulation networks.
Focusing on discrete models of these networks, namely, Boolean automata
networks, we propose to analyse the contribution of non-monotony to the
diversity and complexity in their dynamical behaviours. More precisely, in this
paper, we start by detailing some motivations, both mathematical and
biological, for our interest in non-monotony, and we discuss how it may account
for phenomena that cannot be produced by monotony only. Then, to build some
understanding in this direction, we propose some preliminary results on the
dynamical behaviour of some specific non-monotone Boolean automata networks
called XOR circulant networks.
