Periodic forcing of a model sensory neuron.

We study the effects of sinusoidally modulating the current injected into a model sensory neuron from the weakly electric fish Apteronotus leptorhynchus. This neuron's behavior is known to switch from quiescence to periodic firing to bursting as the injected current is increased. The bifurcation separating periodic from bursting behavior is a saddle-node bifurcation of periodic orbits, and it has been shown previously that there is "type-I burst excitability" associated with this bifurcation, similar to the usual excitability associated with the transition from quiescence to periodic firing. Here we show numerically that sinusoidal modulation of the dc current injected into the model neuron can switch it from periodic to burst firing, or vice versa, depending on the frequency of modulation and the distance to the burst excitability threshold. This is explained by mapping resonance tongues in parameter space. We also show that such a model neuron can undergo stochastic resonance near the transition from periodic to burst firing, as a result of the burst excitability, regardless of the location (soma or dendrite) of the signal and noise. The novelty is that the "output event" is now a burst rather than a single action potential, and the neuron returns to almost periodic firing between bursts, rather than to the vicinity of a fixed point. Since the neuron under study is a sensory neuron that must encode signals with varying temporal structure in the presence of considerable intrinsic noise, these aspects are of potential importance to electrosensory processing and also to other bursting neurons that have periodic input.