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Thelma L. Williams
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Journal Articles
Publisher: Journals Gateway
Neural Computation (1993) 5 (4): 587–596.
Published: 01 July 1993
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Stability against stochastic variation is an important property for biological systems. This paper investigates the robustness of the rhythmic activity produced by a model of the segmental rhythm generator for locomotion in the lamprey, by introducing stochastic properties into the network. In addition, since neuronal models for vertebrate systems often use a single neuron to represent a large class of cells, this paper explores one of the consequences of such reduction, by investigating the effects of duplicating all the cells of the network on its stability against stochastic variation. We have found the basic model network to be very stable, and have found that this stability is increased by doubling the number of cells in the network.
Journal Articles
Publisher: Journals Gateway
Neural Computation (1992) 4 (4): 546–558.
Published: 01 July 1992
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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.