  Patankar schemes have attracted increasing interest in recent years because
they preserve the positivity of the analytical solution of a
production-destruction system (PDS) irrespective of the chosen time step size.
Although they are now of great interest, for a long time it was not clear what
stability properties such schemes have. Recently a new stability approach based
on Lyapunov stability with an extension of the center manifold theorem has been
proposed to study the stability properties of positivity-preserving time
integrators. In this work, we study the stability properties of the classical
modified Patankar--Runge--Kutta schemes (MPRK) and the modified Patankar
Deferred Correction (MPDeC) approaches. We prove that most of the considered
MPRK schemes are stable for any time step size and compute the stability
function of MPDeC. We investigate its properties numerically revealing that
also most MPDeC are stable irrespective of the chosen time step size. Finally,
we verify our theoretical results with numerical simulations.
