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The appearance of so-called exceptional points in the complex spectra ofnon-Hermitian systems is often associated with phenomena that contradict ourphysical intuition. One example of particular interest is the state-exchangeprocess predicted for an adiabatic encircling of an exceptional point. In thiswork we analyse this and related processes for the generic system of twocoupled oscillator modes with loss or gain. We identify a characteristic systemevolution consisting of periods of quasi-stationarity interrupted by abruptnon-adiabatic transitions, and we present a qualitative and quantitativedescription of this switching behaviour by connecting the problem to thephenomenon of stability loss delay. This approach makes accurate predictionsfor the breakdown of the adiabatic theorem as well as the occurrence of chiralbehavior observed previously in this context, and provides a general frameworkto model and understand quasi-adiabatic dynamical effects in non-Hermitiansystems.

General description of quasi-adiabatic dynamical phenomena near exceptional points