An attempt at describing the growth of live organisms by means of a difference-differential equation

Abstract

An attempt is made to create a formal growth model based on a difference-differential equation. The solution of this type of equation is a function of a continuous variable and of a variable assuming natural values. By using the Laplace transformation in respect to time and then solving a specific linear difference equation, a final relation showing the dependence of the amount of dry matter on a natural number and time -- w_n(t), was obtained. This function can be, in a certain sense, a generalization of the known Gregory-Naidenov monomolecular function. For n=1 the function w_n(t) transforms into a relation similar to the Mitscherlich equation, for n>1, its graphs have a characteristic sigmoid shape. Numerical methods are necessary to work out specific forms of the function w_n(t).