Pattern formation of spiral waves in an inhomogeneous medium with small-world connections

Pattern formation of spiral waves in an inhomogeneous excitable medium with small-world connections is investigated. In both cases, with completely local regular connections and with completely random connections, spiral waves cannot survive in the given inhomogeneous medium. It is found that with small-world connections (basically local connections plus a small number of random connections) a well behaved spiral wave can be formed against the destructive role of the inhomogeneous medium. There also exists an optimal fraction of random connections which can greatly enhance the probability of spiral wave formation; this resembles the behavior of stochastic resonance.