Global oscillation mechanism in the stochastic Lotka model

The microscopic one-parameter kinetic model of the oscillatory $A+\overrightarrow{B}2B$ reaction (Lotka model) is studied using direct Monte Carlo simulations and analytical methods. Percolation is proposed as the mechanism of global oscillations that are not limited to any finite size of a system. An analytical estimate of the oscillation frequency is derived and compared to computer simulations. We also observe the transition from synchronized oscillations to specific $f^{-2}$ noise in two dimensions which was previously reported for self-organized critical models.