Nonlinear Dynamical Model of Microorganism Growth in Soil

Abstract

We propose a mathematical description of the soil as a complex dynamical system with components of living, organic and physical nature. The model is a system of partial differential equations of parabolic type with nonlinear sources and nonlinear diffusion. Known oxygen and water dependent feedbacks are described as the sum of variables products: microorganism growth; switching from easily degradable to complex feed substrate; biotic/abiotic/autocatalytic transformations between substances. A selfoscillatory regime with self-organization of stable irregular dynamical structures, in particular the porous space (the the habitat), is detected in the model. The model with linear and nonlinear diffusion reflects processes that occur on different scales. The characteristic size of the problem is determined by the magnitude of the diffusion coefficient, which in capillaries is an order of magnitude lower than in free water. The model makes it possible to describe the macroscopic behavior of the soil system as a whole based on the dynamics of microscale spatially nonhomogeneous structures and allows simulation of various natural soil regimes for which experimental data are available.