Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations.

Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions.

Effect of delayed feedback on the dynamics of a scalar map via a frequency-domain approach.

The effect of delayed feedback on the dynamics of a scalar map is studied by using a frequency-domain approach. Explicit conditions for the occurrence of period-doubling and Neimark-Sacker bifurcations in the controlled map are found analytically. The appearance of a 1:2 resonance for certain values of the delay is also formalized, revealing that this phenomenon is independent of the system parameters.