biostudies-literatureJohn SRUniversity of AucklandNational Science Foundation239-261https://www.ebi.ac.uk/biostudies/studies/S-EPMC10181982biostudies-literatureUnknown51(2)Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model bursting and other activity patterns vary with changes in a timescale associated with the conductance of a fast inward current. Specifically, using numerical simulations and dynamical systems methods, such as fast-sloJournal of computational neuroscienceSlow negative feedback enhances robustness of square-wave bursting.PMC10181982DMS1951095, DMS1612913Osinga HMKrauskopf BJohn SRRubin JEfalseSlow negative feedback enhances robustness of square-wave bursting.Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model bursting and other activity patterns vary with changes in a timescale associated with the conductance of a fast inward current. Specifically, using numerical simulations and dynamical systems methods, such as fast-slo2023-01-01T00:00:00Z2023 May2025-04-26T17:24:24.673Z2025-04-06T15:29:50.256ZS-EPMC101819823706766110.1007/s10827-023-00846-y