It has been known for several decades that electrical alternans occurs during myocardial ischemia in both clinical and experimental work. There are a few reports showing that this alternans can be triggered into existence by a premature ventricular contraction. Detriggering of alternans by a premature ventricular contraction, as well as pause-induced triggering and detriggering, have also been reported. We conduct a search for triggered alternans in an ionic model of ischemic ventricular muscle in which alternans has been described recently: a one-dimensional cable of length 3 cm, containing a central ischemic zone 1 cm long, with 1 cm segments of normal (i.e., nonischemic) tissue at each end. We use a modified form of the Luo-Rudy [Circ. Res. 68, 1501-1526 (1991)] ionic model to represent the ventricular tissue, modeling the effect of ischemia by raising the external potassium ion concentration ([K(+)](o)) in the central ischemic zone. As [K(+)](o) is increased at a fixed pacing cycle length of 400 ms, there is first a transition from 1:1 rhythm to alternans or 2:2 rhythm, and then a transition from 2:2 rhythm to 2:1 block. There is a range of [K(+)](o) over which there is coexistence of 1:1 and 2:2 rhythms, so that dropping a stimulus from the periodic drive train during 1:1 rhythm can result in the conversion of 1:1 to 2:2 rhythm. Within the bistable range, the reverse transition from 2:2 to 1:1 rhythm can be produced by injection of a well-timed extrastimulus. Using a stimulation protocol involving delivery of pre- and post-mature stimuli, we derive a one-dimensional map that captures the salient features of the results of the cable simulations, i.e., the {1:1-->2:2-->2:1} transitions with {1:1<-->2:2} bistability. This map uses a new index of the global activity in the cable, the normalized voltage integral. Finally, we put forth a simple piecewise linear map that replicates the {1:1<-->2:2} bistability observed in the cable simulations and in the normalized voltage integral map. (c) 2002 American Institute of Physics.