Excitable media are systems which are at rest in the absence of external input but which respond to a sufficiently strong stimulus by sending a wave of "excitation" across the medium. Examples include cardiac and cortical tissue, and in each of these examples rotating spiral waves have been observed and associated with abnormalities. How such waves are initiated is not well understood. In this numerical study of a standard mathematical model of excitable media, we obtain spirals and other oscillatory patterns by a method, simple in design, which had previously been ruled out. We analyze the early stages of this process and show that long term stable oscillatory behavior, including spiral waves, can start with very simple initial conditions, such as two small spots of excitation, and no subsequent input.  For this model system, we find that random stimulation produces stable oscillations relatively often. In our model system, self-sustained patterns of excitation are generated with some frequency by random stimulation, leading us to suggest that such patterns could appear spontaneously in living tissue , either cardiac or neural, with negative consequences .
Excitable media are systems which are at rest in the absence of external input but which respond to a sufficiently strong stimulus by sending a wave of "excitation" across the medium. Examples include cardiac and cortical tissue, and in each of these examples rotating spiral waves have been observed and associated with abnormalities. How such waves are initiated is not well understood. In this numerical study of a standard mathematical model of excitable media, we obtain spirals and other oscillatory patterns by a method, simple in design, which had previously been ruled out. We analyze the early stages of this process and show that long term stable oscillatory behavior, including spiral waves, can start with very simple initial conditions, such as two small spots of excitation, and no subsequent input. Thus, there are no refractory cells in the initial condition. For this model , even random spots of stimulation result in periodic rotating patterns relatively often, leading us to suggest that this could happen in living tissue .
A
Thus, there are no refractory cells in the initial condition.
R
system, we find that random stimulation produces stable oscillations relatively often. In our model system, self-sustained patterns of excitation are generated with some frequency by random stimulation,
, even random spots of stimulation result in periodic rotating patterns relatively often,
R
such patterns could appear spontaneously
this could happen
D
, either cardiac or neural, with negative consequences