Oscillatory patterns in an autocatalytic reaction ring network simulated by a probabilistic cellular automaton

A two dimensional probabilistic cellular automaton is presented. It simulates a reaction-diffusion process occurring in biomembranes during active transport described by an autocatalytic ring network. The automaton suffers a transition from a completely disordered state to a state with well defined oscillations and spatial inhomogeneous patterns by changing the parameters. The different dynamic states have been characterized by means of Fourier transforms of concentration time evolution and through the definition of an agglomeration parameter. Vacancy concentration and lattice size effects are analyzed.