An organism growth model optimised for soybean under arbitrary function of the external conditions

A growth model adapted for an agricultural crop (soybean) is presented. From the mathematical point of view, the growth process is presented by a particular dynamical system, consisting of two ordinary differential equations. The calculated crop growth curves show remarkable smoothness, although the real growth process is usually subject to various environmental influences. A characteristic function, the first integral of the system of equations, is shown to exist, which is in good correspondence with the observed stability of the real growth process. The important feature of our dynamical system is that the first integral does not depend on the function (bounded and continuous), describing the external impacts. The model is presented in two forms. Using the first integral, the system of equations is transformed into a specific form of Verhulst equation. Here, the function of the external influences is presented in integral form. This model ensures the slow down of the growth curves after the vegetative stage which is usually the problem for the use of Verhulst equation in organism level growth analysis. In the hypothetical case of absence of external impacts, this model is reduced to the well-known form of Verhulst equation. The model has been tested using soybean field experimental data which has shown quite acceptable results. Some preliminary conclusions on the model’s abilities are briefly discussed.