Degradation of lignocellulose by fungi based on differential equation

Abstract

In this paper, we studied the decomposition of plant materials and lignocellulosic fibers by fungi, and the relationship between some characteristics of fungi. And established several mathematical models to solve the problems raised in the problem. Firstly, in the case of the coexistence of different fungi, ignoring the interaction between them, we use differential equation and Monod equation to establish the model. In the model, the decomposition rate of each fungus to plant materials and lignocellulosic fibers at a different time and the mycelial elongation rate of the fungus itself can be obtained. In the model solving, the ode instruction is used to solve the differential equations, and the variable step Runge Kutta Feldberg method is used to improve the accuracy. Then we considered the interactions between different fungi: mutual promotion and mutual inhibition. Different fungi have different moisture tolerance, so they have different decomposition rates of plant materials and wood fibers. By using logistic law, our model can describe the decomposition ability of different interactions between fungi to decompose lignocellulosic fibers. After solving the model, it is found that the fungi that promote each other are the fastest, the fungi that do not affect each other are the second, and the fungi that inhibit each other are the slowest, that is, the decomposition rate is the smallest.