SIMPLE-MODELS FOR EXCITABLE AND OSCILLATORY NEURAL NETWORKS

Chains of coupled oscillators of simple ''rotator'' type have been use d to model the central pattern generator (CPG) for locomotion in lampr ey, among numerous applications in biology and elsewhere. In this pape r, motivated by experiments on lamprey CPG with brainstem attached, we investigate a simple oscillator model with internal structure which c aptures both excitable and bursting dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin-Huxley equations a nd two-variable simplifications thereof. We analyse pairs of coupled o scillators with both excitatory and inhibitory coupling. We also study traveling wave patterns arising from chains of oscillators, including simulations of ''body shapes'' generated by a double chain of oscilla tors providing input to a kinematic musculature model of lamprey.