A NOTE ON A HYPOTHETICAL PIECEWISE SMOOTH SIGMOIDAL GROWTH FUNCTION: REACTION NETWORK ANALYSIS, APPLICATIONS

Abstract

Typically, the researcher is faced with the following dilemma whenanalyzing and approximating data (in practice - grouped data): How, in a fixed modelin the field of Growth Theory with parameters: Ai, i = 0, 1, . . . n ( for which thereis a theoretical, substantiated justification for good modeling of the studied dynamicmodel), to obtain an adequate analytical continuation when the dynamics of the ob-served model changes at t > t1, whereby a lower (respectively higher) asymptotic satu-ration is achieved from what the basic model offers, but with the same fixed parameters:Ai, i = 0, 1, . . . n. In attacking this topical issue (related to data approximation andmodeling in the field of Population Dynamics and Debugging Theory, etc.), researchhas been conducted related to:

• the possibility for smooth stitching of sigmoidal functions with fractionally ratio-nal argument;

• providing researchers (who are not necessarily specialists - mathematicians andcomputer scientists) with reliable software tools for statistical analysis of specificdata;

• the possibility to describe the mentioned ”analytical extensions” in terms of thereaction-kinetic mechanisms - as solutions of reaction systems from differentialequations.