  In this paper we consider piecewise affine differential equations modeling
gene networks. We work with arbitrary decay rates, and under a local hypothesis
expressed as an alignment condition of successive focal points. The interaction
graph of the system may be rather complex (multiple intricate loops of any
sign, multiple thresholds...). Our main result is an alternative theorem
showing that, if a sequence of region is periodically visited by trajectories,
then under our hypotheses, there exists either a unique stable periodic
solution, or the origin attracts all trajectories in this sequence of regions.
This result extends greatly our previous work on a single negative feedback
loop. We give several examples and simulations illustrating different cases.
