Lattice limit cycle dynamics: Influence of long-distance reactive and diffusive mixing

The properties of global oscillations produced by coupled reactive stochastic discrete systems on a 2D lattice support are studied, taking into account the competitive influence of local and global mixing processes. Two types of global mixing are considered: reactive and diffusive. It is shown that in the case of diffusive mixing the increase in the diffusive coupling leads to a corresponding increase in the amplitude of the global oscillations. In the case of reactive mixing the competition of local-to-global effects leads to unexpected complex phenomena. Kinetic Monte Carlo simulations demonstrate that the amplitude of oscillations as a function of the mixing-reactive coupling presents an optimal value, which is attributed to the competitive effects between the local and global processes