Mathematical models of central pattern generators in locomotion: II. Single limb models for locomotion in the cat

Three mathematical models of central pattern generation for locomotion in the single limb of the cat are presented. In each model, the activities in populations of neurons controlling limb joint flexors and extensors are described by a system of nonlinear differential equations. Each solution of the system for a different set of parameters corresponds to a simulation of some gait of the cat. Model I is based on unit generators for each limb joint muscle group and assumes that flexors inhibit their paired extensors, but not vice-versa. Model IIa assumes that flexors and extensors are mutually inhibitory, but that only the flexors have inherent oscillatory capability. Model IIb assumes flexors and extensors are mutually inhibitory and that both flexors and extensors have oscillatory capability. The properties of each of these models are explored, compared and contrasted, and discussed in relation to the experimental literature. All three models are shown to be capable of generating patterns consistent with various stepping rates of the cat and to show appropriate muscle sequencing and flexor-extensor interactions. Further, all three models exhibit smooth initiation and termination of stepping. However, Model I seems to provide a more parsimonious account of producing changes in stepping rate and is preferred, therefore, over models IIa and IIb.