Spiral wave in an inhomogeneous excitable medium

Using a Barkley model as an example, the pattern formation of spiral waves in inhomogeneous excitable medium is investigated. The normal distribution of parameters fluctuations is introduced to depict the inhomogeneous medium. It is found that the parameter fluctuations play an important role in the formation of spiral pattern. For a larger variance of the parameter fluctuations, the spiral waves are rough. In the case of the uniform distribution of fluctuations in two parameters, spiral wave cannot be observed for fluctuations beyond a certain range. It is conjectured that these results are induced by the rotating frequency of spiral wave for different parameters. For the larg rotating frequency, the spiral wave pattern is finely crowded, while it is sparse for small frequencies.