Orbit spectral density versus stimulus identity and intensity.

A concept of orbit spectral density for a one-dimensional iterated function is presented. To compute orbit spectral density, a method of extracting low-order periodic orbits from the dynamical system defined by the iterated function is first used. All points of the dynamics are then partitioned among the periodic orbits according to a distance measure. Partition sizes estimate the density of trajectories around periodic orbits. Assigning these trajectory densities to the orbit indexes introduces the orbit spectral density. A practical computational example is presented in the context of a model olfactory system.