Transient response of the Geman-Miller respiratory oscillator model

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Abstract
Recent evidence suggests that there is a persistence of elevated respiratory center activity for many respiratory cycles after the cessation of a neural stimulus. To explore the theoretical possibility that this behavior may be a consequence of the neural oscillator that dictates respiratory rhythm, the transient response of a mathematical model of a medullary respiratory oscillator recently described by Geman and Miller was examined using computer simulation. This concept was motivated by the presence of a persistent transient response behavior inherent in oscillators from mathematical physics. The results indicate that a transient persistence effect is evident in the model behavior under some conditions, and this effect as well as the steady-state amplitude is markedly sensitive to the shape of the saturation function that interconnects the neuron populations. Furthermore, this behavior is initiated by either an abrupt decrease in a tonic input or an abrupt decrease in the synaptic weights connecting subpopulations of neurons.

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