Ring dynamics and percolation in an excitable medium

URL:

Abstract:

Statistical properties of the pattern formation process in excitable media are studied with the aid of a simple automaton model for the dynamics. When a quiescent medium is excited at local, randomly placed regions in the fluid, "rings" of excitation propagate through the medium. The evolution is studied as a function of the initial seeding probability of the locally excited regions and a scaled picture of the dynamics is presented, which holds for arbitrary dimensions of the medium. High initial seeding probabilities or the increase in the fraction of the medium which is excited as a result of the growth of the rings can lead to large connected regions of excitation in the medium. This process can be studied as a dynamical percolation problem. The percolation thresholds, where a connected region spans the system with certainty, are given as a function of the seeding probability and the time. At percolation the spatial configuration of the excited region possesses a fractal dimension of D=1.9. Chemically reacting systems which exhibit excitability, like the Belousov-Zhabotinskii reaction, are good candidates for the experimental observation of the phenomena described here. © 1986 American Institute of Physics.