Modelling the Emergence and Dynamics of Perceptual Organisation in Auditory Streaming
Figure 5
Dynamical system formed in response to an ABA− sequence.
A and B) Collision and success rate effects shown on the excitation/inhibition (dynamics, top; see Figure 4) and the sound-group depiction (chains, bottom; see Figure 2) of the chains formed in response to a repeating ABA− sequence. Columns represent the three most stable chains formed: ABA−←, A−←, and −B−−←, from left to right. DYNAMICS (top panels): The inhibitory neuronal population is shown at the top, the excitatory one at the bottom of the panel. The strength of each population is marked by the filling of the circles (empty circle = weak, filled circle = strong). The size of the suppressing effect of the inhibitory population on the excitatory one is marked by the width of the blue line connecting them. The inhibitory population of a chain is strengthened by collisions with other chains (see section “Successes (S) and Collisions (C)”); the number of collisions and the amount of strengthening they provide to the inhibitory population of the given chain are noted over the inhibitory population. The effects of collisions are marked by red arcs connecting the excitatory population of each chain with the inhibitory population of those chains with which it collides (A−← and −B−−← don't collide, all other pairs do). The size of the strengthening effect to the inhibitory neuronal population (dependent on the strength of the excitatory population of the other colliding chain) is marked by the width of the arc. Excitation is strengthened by the rate of successful predictions made by the given chain; the number of successful predictions is noted below the excitatory population. For simplicity, the rediscovery, noise and self-excitation terms are not depicted here. Chains (bottom panels): Blue shading marks the currently dominant chain (i.e., the chain(s) whose excitatory population is stronger than that of the other chains). A) Integrated organisation dominant. Whilst the ABA−← chain dominates, the excitatory activity associated with the A−← and −B−−← chains is low. B) Segregated organisation dominant. Whilst the A−← and −B−−← chains dominate, the excitatory activity associated with the ABA−← chain is low. The events in the A−← and −B−−← chains do not collide with each other, so they have no inhibitory effect on each other. C) System state showing the various trajectories that the variables associated with the three chains (represented by and marked on the three axes) take, given 20 randomly-chosen initial values (green dots). In the absence of noise, the system permanently settles into one of the two organisations associated with diagrams in (A) and (B) (red dots), moving along a deterministic trajectory (blue lines). That is, some time after the start of the sequence either ABA−← becomes highly excited with A−← and −B−−← becoming weak (lower left red dot) or vice versa (upper right red dot) and the excitation and inhibition values of the three chains do not change anymore (i.e., the model without a noise effect would predict stable perception).