Linear Analysis of the Central Pattern Generation Mechanism

A new model is presented for the central pattern generation mechanism based on the integrate-and-fire (IF) model and the neuronal synaptic transfer function. Unlike the existing models which either use complex nonlinear equations or totally ignore the spike (action potential) generation mechanism of a real neuron, the new model presents a more realistic form of the CPG and its neuronal interactions. The most important feature of this model is that it converts the CPG to a linear network for further analysis despite the fact that the IF model is a nonlinear system. This particularly allows us to use well-known feedback theories to obtain the condition and frequency of oscillation in the burst activity of a CPG.