  It has been reported in the literature that the survival probability $P(t)$
near an exceptional point where two eigenstates coalesce should generally
exhibit an evolution $P(t) \sim t^2 e^{-\Gamma t}$, in which $\Gamma$ is the
decay rate of the coalesced eigenstate; this has been verified in a microwave
billiard experiment [B. Dietz, et al, Phys. Rev. E 75, 027201 (2007)]. However,
the heuristic effective Hamiltonian that is usually employed to obtain this
result ignores the possible influence of the continuum threshold on the
dynamics. By contrast, in this work we employ an analytical approach starting
from the microscopic Hamiltonian representing two simple models in order to
show that the continuum threshold has a strong influence on the dynamics near
exceptional points in a variety of circumstances. To report our results, we
divide the exceptional points in Hermitian open quantum systems into two cases:
at an EP2A two virtual bound states coalesce before forming a resonance,
anti-resonance pair with complex conjugate eigenvalues, while at an EP2B two
resonances coalesce before forming two different resonances. For the EP2B,
which is the case studied in the microwave billiard experiment, we verify the
survival probability exhibits the previously reported modified exponential
decay on intermediate timescales, but this is replaced with an inverse power
law on very long timescales. Meanwhile, for the EP2A the influence from the
continuum threshold is so strong that the evolution is non-exponential on all
timescales and the heuristic approach fails completely. When the EP2A appears
very near the threshold we obtain the novel evolution $P(t) \sim 1 - C_1
\sqrt{t} + D_1 t$ on intermediate timescales, while further away the parabolic
decay (Zeno dynamics) on short timescales is enhanced. We also discuss the
parametric encirclement of the EP2A in an appendix.
