Stability and Intermittency in Large-Scale Coupled Oscillator Models for Perceptual Segmentation

Abstract

The coupled map lattice, a system of locally coupled nonlinear maps, is proposed as a model for perceptual segmentation. Patterns of synchronized activity are obtained in the model from high-dimensional, deterministic chaos. These patterns correspond to segmented topographical mappings of the visual field. The chaotic dynamic has a dual role of contributing to pattern creation in unsynchronized states and of noise revolting against stabilization in synchronized states. The dynamic allows rapid transitions between unsynchronized and synchronized states. Their stability characteristics are explored using analytical tools and numerical simulations. Stability or instability are shown to be determined by network coupling strength, in proportion to the rate of chaotic divergence. The introduction of adaptive connections, in combination with stimulus-controlled oscillation, enables stable or meta-stable patterns of synchronized activity to occur, depending on the perceptual structure in the visual field. For a perceptually ambiguous pattern, the system switches between alternative meta-stable segmentations. The switching-time distribution obtained from the model was found in agreement with those observed in the experimental literature. Copyright 1997 Academic Press. Copyright 1997 Academic Press