Electrosensory Dynamics: Dendrites and Delays

Pyramidal cells in the electrosensory lateral line lobe (ELL) of weakly electric fish have been observedto produce high-frequency burst discharge with constant depolarizing current (Turner et al., 1994). We present a two-compartment model of an ELL pyramidal cell that produces burst discharges similar to those seen in experiments.The burst mechanism involves a slowly changing interaction between the somatic and dendritic action potentials.Burst termination occurs when the trajectory of the system is reinjected in phase space near the “ghost” of a saddle-node bifurcation of fixed points. The burst trajectory reinjection is studied using quasi-static bifurcation theory,that shows a period doubling transition in the fast subsystem as the cause of burst termination. As the applieddepolarization is increased, the model exhibits first resting, then tonic firing, and finally chaotic bursting behavior,in contrast with many other burst models. The transition between tonic firing and burst firing is due to a saddle-nodebifurcation of limit cycles. Analysis of this bifurcation shows that the route to chaos in these neurons is type Iintermittency, and we present experimental analysis of ELL pyramidal cell burst trains that support this modelprediction. By varying parameters in a way that changes the positions of both saddle-node bifurcations in parameterspace, we produce a wide gallery of burst patterns, which span a significant range of burst time scales.