Dynamical symmetries and temporal segmentation

Segmentation of a mixed input into recognizable patterns is a task that is common to many perceptual functions. It can be realized in neural models through temporal segmentation: formation of staggered oscillations such that within each period every nonlinear oscillator peaks once and is dominant for a short while. We investigate such behavior in a symmetric dynamical system. The fully segmented mode is one type of limit cycle that this system can exhibit. We discuss its symmetry classification and its dynamical characterization. We observe that it can be sustained for only a small number of segments and relate this fact to a limitation on the appearance of narrow subharmonic oscillations in our system.