On Chaotic Subthreshold Oscillations in a Simple Neuronal Model

Abstract

Abstract. In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, a sequence of period-doubling bifurcations for small-scale oscillations precedes the transition into the spiking regime. For a wide range of values of the timescale separation parameter, this scenario is recovered numerically. Its relation to the singularly perturbed integrable system is discussed.

Voltage Interval Mappings for an Elliptic Bursting Model

“…Using the mappings of higher degrees we can evaluate the critical moments at which the period-two and period-four orbits are about to bifurcate. We point out that a period-doubling cascade, beginning with a limit cycle near the Hopf-initiated canard toward subthreshold chaos has been recently reported in slow-fast systems [30,31].…”