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We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The particle density and the global reaction rate are also shown analytically and numerically on a two-dimensional square lattice with the periodic boundary conditions. Especially, the crossover of the global reaction rate is discussed in both early-time and long-time regimes.Comment: 6 pages, 3 figures, Late

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A one-dimensional iterative map with two control parameters — the Kim–Kong map — is proposed. Our purpose is to investigate the characteristic properties of this map, and to discuss numerically the multifractal behavior of the normalized first passage time. Based especially on the Monte Carlo simulation, the normalized first passage time to arrive at the absorbing barrier after starting from an arbitrary site is mainly obtained in the presence of both absorption and reflection on a two-dimensional Sierpinski gasket. We also discuss the multifractal spectra of the normalized first passage time, and the numerical result of the Kim–Kong model presented will be compared with that of the Sinai and logistic models.