We compare the behaviour of two models describing rate-dependent
activity in cardiac cells and neurons, respectively.  The phenomenon
known as triggered activity in the cardiac literature is quite similar
to a phenomenon seen in a crab neuron, dubbed spontaneous secondary
spiking by Tom Kepler and Eve Marder.  Ordinarily, one injected current
pulse will induce a single action potential.  However, a train of such
action potentials may be followed by some "extra" or "spontaneous"
action potentials depending on the frequency and length of the initial
train of action potentials.  These extra action potentials are referred
to as triggered activity or spontaneous secondary spikes, depending
on the application.  We will explain how these extra action potentials
arise and point out the similarities and differences of the two models.