The current evolution of transportation technology makes efficient management and planning of very large networks technically feasable. Modelling the dynamics of traffic in regional-sized network is a difficult task. Traffic dynamics in a network result from two competing processes which constitute dynamic traffic assignment (DTA): i) the departure time, mode and route choice of travellers, which define the travel demand, and ii) the supply of the network, which proceeds from the physical capacity of infrastructures and from the quantity of travellers using the infrastructure, i.e. the congestion of the infrastructure. The first idea of this paper is to curb the exponential complexity of DTA in a very large network by simplifying the representation of the traffic flow. To this purpose we use a bidimensional macroscopic model of traffic flow on the network. The proposed model will be introduced in its discretized phenomenological aspect, the AIBM ( the (an)isotropic bidimensional model). The second idea of the paper is that travellers carry out their route choice based on the instantaneous travel cost which expresses the current state of the network, whereas they make their departure time choice with respect to their desired arrival time and based on the predictive OD (origin-destination) travel cost. It is shown that the AIBM model can adequately represent the travellers’ choice process. Finally the evolution of the network subjected to day-to-day traveller choices, will be analyzed. It will be shown that depending on the travellers’ learning strategy this process may converge to one or several equilibria, or result in periodic orbits, as well as fluctuations of increasing time-scale and irregular orbits. All this results suggest possible chaotic behavior, consistently with previous studies carried out in much simpler contexts.