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The evolution of domain structure is investigated in a two-dimensional voter model with three states under cyclic dominance. The study focus on the dynamics of vortices, defined by the points where the three states (domains) meet. We can distinguish vortices and antivortices which walk randomly and annihilate each other. The domain wall motion can create vortex-antivortex pairs at a rate that is increased by the spiral formation due to cyclic dominance. This mechanism is contrasted with a branching annihilating random walk (BARW) in a particle-antiparticle system with density-dependent pair creation rate. Numerical estimates for the critical indices of the vortex density [beta=0.29(4)] and of its fluctuation [gamma=0.34(6)] improve an earlier Monte Carlo study [K. Tainaka and Y. Itoh, Europhys. Lett. 15, 399 (1991)] of the three-state cyclic model in two dimensions.

Vortex dynamics in a three-state model under cyclic dominance