Figure 6.

A cognitive view of associative learning as offered by the tools of dynamical systems. Each panel illustrates the flow together with the phase portrait of the GRN in the space of p and w2 (the w1 axis is ignored for conciseness, since it is not informative). Here, ‘response’ represents the concentration levels of p. The red and green curves in the top and bottom panels, respectively, depict representative trajectories. The red and green trajectories are each split over time across the horizontal panels in their respective rows, as depicted by grey dashed lines connecting the consecutive pieces whose endpoints are marked by colour filled circles. Note that the endpoint of one piece and the starting point of the following piece are of the same colour since they represent the same states. The overall initial state of the two trajectories (green filled circle) are the same. Also shown in each panel are the stable equilibrium and saddle points. The top panels show CS alone cannot evoke a response (red trajectory eventually reaches a low-response state in panel (c)). The bottom panels show that following an association of CS with US, CS alone can evoke a response (the green trajectory eventually reaches a high-response state in panel (f)). Notice that there are two attractors (hence two basins of attraction) when CS alone is applied (right panels). In the dynamical systems view, associative learning is about steering the internal state associated with CS (w2) into the basin of attraction associated with high value of p with the help of application of US. More specifically, a minimum value of w2 is necessary and sufficient to evoke a high response; this is termed the ‘learning threshold’ (the black dashed line in panels (a,c,f)). Here, associative learning is accomplished by w1 ‘shepherding’ w2 above the learning threshold.