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We study fast-slow maps obtained by discretization of planar fast-slowsystems in continuous time. We focus on describing the so-called delayed lossof stability induced by the slow passage through a singularity in fast-slowsystems. This delayed loss of stability can be related to the presence ofcanard solutions. Here we consider three types of singularities: transcritical,pitchfork, and fold. First, we show that under an explicit Runge-Kuttadiscretization the delay in loss of stability, due to slow passage through atranscritical or a pitchfork singularity, can be arbitrarily long. In contrast,we prove that under a Kahan-Hirota-Kimura discretization scheme, the delayedloss of stability related to all three singularities is completely symmetric inthe linearized approximation, in perfect accordance with the continuous-timesetting.

Extended and symmetric loss of stability for canards in planar fast-slow maps