Phase Coupling in Simulated Chains of Coupled Oscillators Representing the Lamprey Spinal Cord

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Abstract
Previous application of a mathematical theory of chains of coupled oscillators to the results of experiments on the lamprey spinal cord led to conclusions about the mechanisms of intersegmental coordination in the lamprey. The theory provides no direct link, however, to electrophysiological data obtained at the cellular level, nor are the details of the neuronal circuitry in the lamprey known. In this paper, a variant of the theory is developed for which the relevant variables can potentially be measured. This theory will be applied to measurements on simulated oscillators, based on a network that has been postulated to constitute the basic circuitry of the segmental oscillator in the lamprey. A linear approximation to the equations is derived, and it will be shown that the behavior of simulated chains of these oscillators obeys the predictions of this approximation.