Figure 4

Predicted perceptual behaviour in a volatile environment. (a) Representative example of simulated dynamics of fitted model: activities \(r_1\), \(r_2\) and adaptive states \(a_1\), \(a_2\) driven by intrinsic noise \(n_1\), \(n_2\) and variable sensory inputs \(I_1\) and \(I_2\). In a volatile environment, reversals (defined by \(r_1=r_2\)) may be triggered externally (differential input \(\Delta I=I_1-I_2\)) or internally (differential adaptive state \(\Delta a=a1-a2\)) or both. Competition strength was fixed at \(\beta =3\). To assess reversal initiation, we distinguished between transition periods (yellow stripes, 20 ms before and after \(r_1=r_2\)), immediately preceding periods (purple stripes, 40 to 21 ms before \(r_1=r_2\)), and all other times. (b) Based on this classification, we computed the conditional likelihood of reversals (coloured contours) as a function of \(\Delta I\) and \(\Delta a\) values during initiation periods, in the vicinity of the median \(\Delta I\) and \(\Delta a\) values (over all periods, red dot). In this vicinity, the reversal probability grows exponentially in a particular direction (red dashed line). The length of the gradient vector \(\partial \ln \,P(\Delta I\), \(\Delta a)\) represents the ‘sensitivity’ of reversal probability to \(\Delta I\) and/or \(\Delta a\) values, and the ‘exploration’ angle \(\alpha\) represents the relative influence of internal state \(\Delta a\), compared to external state \(\Delta I\) (external state). A larger value implies that the system responds less consistently to external state, behaving in a more explorative manner. (c) Enlarged cut through the \(\ln _{}P(\Delta I\), \(\Delta a)\) surface in the direction of the the gradient vector (red arrow), showing the neutral level (defined by \(\Delta I=\Delta a=0\), black dashed line) and median level (red dashed line). The distance between levels (blue arrow), represents ‘stability’ and measures the stabilizing or destabilizing effect of external and internal median states. For positive values (within green area), median states lower reversal probability, stabilizing the percept; vice versa for negative values (within grey area). (d, e) Developmental and maturational trajectories of predicted perceptual parameters (stability, sensitivity, exploration) for females (d) and males (e). Mean values (coloured dots), peak age of maturation index (red stars), and confidence intervals (standard deviations, grey volumes).