A Lotka-type model for oscillations in surface reactions

Global oscillation mechanism in the stochastic Lotka model

The microscopic one-parameter kinetic model of the oscillatory A+B-->2 B 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.

Monte Carlo simulations for a Lotka-type model with reactant surface diffusion and interactions

The standard Lotka-type model, which was introduced for the first time by Mai et al. [J. Phys. A 30, 4171 (1997)] for a simplified description of autocatalytic surface reactions, is generalized here for a case of mobile and energetically interacting reactants. The mathematical formalism is proposed for determining the dependence of transition rates on the interaction energy (and temperature) for the general mathematical model, and the Lotka-type model, in particular. By means of Monte Carlo computer simulations, we have studied the impact of diffusion (with and without energetic interactions between reactants) on oscillatory properties of the A+B-->2B reaction. The diffusion leads to a desynchronization of oscillations and a subsequent decrease of oscillation amplitude. The energetic interaction between reactants has a dual effect depending on the type of mobile reactants. In the limiting case of mobile reactants B the repulsion results in a decrease of amplitudes. However, these amplitudes increase if reactants A are mobile and repulse each other. A simplified interpretation of the obtained results is given.

Monte carlo simulations of the periodically forced autocatalytic A+B-->2B reaction

The one-parameter autocatalytic Lotka-like model, which exhibits self-organized oscillations, is considered on a two-dimensional lattice, using Monte Carlo computer simulations. Despite the simplicity of the model, periodic modulation of the only control parameter drives the system through a sequence of frequency locking, quasiperiodic, and resonance behavior.