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].…”

The Dud Canard: Existence of Strong Canard Cycles in R3

“…Finally, [49] studies a Fitz-Hugh-Nagumo-like system and demonstrates, also through numerical computations, that the Hopf cycles lose stability via a sequence of period-doubling bifurcations. Interestingly, the cascade follows the Feigenbaum constant for conservative systems for small values of > 0.…”

“…In particular, we are interested in a description of the period doubling bifurcations that have been reported in several papers, see e.g. [49]. These period doubling bifurcations are associated with the heteroclinic connection on the blowup sphere (recall Fig.…”