that we use a simple enough model. Understanding of the Dimits shift is already complicated when we study the modified Hasegawa–Wakatani model in [@Zhu20], when we observed the presence of avalanche-like structures, which are not supported by the mTHE. Furthermore, the recent paper by [@Ivanov20] shows that avalanches themselves can become intricate when additional physics from finite ion temperature is taken into account. This complicates the problem even further, and more work remains to be done to understand the Dimits shift in the general case. Our paper is intended as one of the first steps in that direction.

This paper is organized as follows. In section \[sec:mTHE\] we introduce the mTHE. In section \[sec:Linear\] we describe the primary, the secondary, and the tertiary instability within the mTHE. In section \[sec:TIcalculation\] we analytically derive the TI growth rate using two different approaches mentioned above. In section \[sec:DSPrediction\] we derive an analytic prediction of the Dimits shift. Finally, a brief introduction of the WME and phase-space trajectories are presented in Appendices \[appA\] and \[appB\].

Modified Terry–Horton equation {#sec:mTHE}
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The mTHE can be considered as a minimal model that simultaneously captures the primary, secondary, and tertiary instabilities. It is a two-dimensional scalar 