model is perhaps the simplest phenomenological model that can describe how sheared flows help achieve a high-confinement regime [@Diamond94; @Malkov01; @Kim03; @Kobayashi15]. However, this paradigm may be oversimplified. For example, while direct simulations show that ZFs saturate at finite amplitude even in collisionless plasma [@Rogers00; @St-Onge17], the predator–prey model predicts otherwise. This is because the predator–prey model assumes statistically homogeneous turbulence, and this assumption is inapplicable in the Dimits regime, where strong ZFs are present and turbulence is inhomogeneous.

A more elaborate approach to understanding the Dimits shift was based on the concept of the “tertiary” instability (TI) [@Rogers00; @Rogers05]. The idea is that if ZFs are subject to the TI, then turbulence cannot be completely suppressed by ZFs and the Dimits regime ends. Despite some criticism [@Kolesnikov05], this explanation is widely accepted. However, the understanding of the TI and the Dimits shift has been largely qualitative, arguably because these effects have not been widely studied within simple enough models.

Recently, [@St-Onge17] proposed the modified Terry–Horton equation (mTHE) as a minimal model that captures the Dimits shift. @St-Onge17 calculated the TI growth rate using four-mode truncation (4MT) and derived a sufficient condition for ZFs to be stable within the mTHE. 