Mathematical modeling of oscillations in a Lotka reaction on a catalyst surfaceстатья
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Дата последнего поиска статьи во внешних источниках: 4 февраля 2014 г.
Аннотация:The article investigates a two-component heterogeneous-catalytic reaction on a catalyst surface with a regular square lattice. This reaction is an analog of the three-dimensional Lotka “predator–prey” reaction. The reaction kinetic scheme is applied to construct a hierarchical system of mathematical models,starting with a micro-level stochastic model and up to macro-level models. Two ODE systems are proposed with pair probabilities allowing for bounded diffusion rate of one of the reaction components. These systems display self-exciting oscillations under certain conditions. A parametric analysis of the pair probability models is carried out and self-exciting oscillation regions are determined in the parameter space. The solutions of these systems are compared with the dynamics of the microscopic stochastic model simulated by the dynamic Monte Carlo method. Conditions for the appearance of oscillations on the macro level are found.
Keywords: Lotka–Volterra system, microscopic stochastic model, Monte Carlo method, ODE system
with pair probabilities, self-exciting oscillations, bifurcation analysis.