Canards of mixed type in a neural burster

Abstract

Canards are solutions of slow-fast systems that spend long times near branches of repelling equilibria, periodic orbits, or higher-dimensional invariant sets. Here, we report on the observation of a new type of canard orbit, labeled a canard of mixed type. This canard orbit is a hybrid of the classical limit cycle canards, which spend long times near attracting and repelling branches of equilibria, and torus canards, which spend long times near attracting and repelling branches of periodic orbits. The canards of mixed type arise in a model of neural bursting activity of fold-fold cycle type, and, as other canard phenomena, separate different dynamic states.