Open AccessAn attempt at describing the growth of live organisms by means of a difference-differential equation
Author(s) -
A. Gregorczyk
Publication year - 2014
Publication title -
acta societatis botanicorum poloniae
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.297
H-Index - 29
eISSN - 2083-9480
pISSN - 0001-6977
DOI - 10.5586/asbp.1986.044
Subject(s) - mathematics , differential equation , function (biology) , generalization , variable (mathematics) , sigmoid function , laplace transform , transformation (genetics) , laplace's equation , green's function for the three variable laplace equation , mathematical analysis , partial differential equation , chemistry , computer science , biochemistry , evolutionary biology , machine learning , artificial neural network , gene , biology
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 -- wn(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 wn(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 wn(t)