  We propose the use of Deterministic Generalized Asynchronous Random Boolean
Networks [Gershenson, 2002] as models of contextual deterministic discrete
dynamical systems. We show that changes in the context have drastic effects on
the global properties of the same networks, namely the average number of
attractors and the average percentage of states in attractors. We introduce the
situation where we lack knowledge on the context as a more realistic model for
contextual dynamical systems. We notice that this makes the network
non-deterministic in a specific way, namely introducing a non-Kolmogorovian
quantum-like structure for the modelling of the network [Aerts, 1986]. In this
case, for example, a state of the network has the potentiality (probability) of
collapsing into different attractors, depending on the specific form of lack of
knowledge on the context.
