Mathematical Analysis of Some Reaction Networks Inducing Biological Growth/Decay Functions.

Abstract

In this work, we study some characteristics of sigmoidal growth/decay functions that are solutions of dynamical systems. In addition, the studied dynamical systems have a realization in terms of reaction networks that are closely related to the Gompertzian and logistic type growth models. Apart from the growing species, the studied reaction networks involve an additional species interpreted as an environmental resource. The reaction network formulationВ of the proposed models hints forВ the intrinsic mechanism of the modeled growthВ process and can be used for analyzing evolutionaryВ measured data when testing various appropriateВ models, especially when studying growth processesВ in life sciences. TheВ proposed reaction network realization of GompertzВ growth model can be interpreted from the perspectiveВ of demographic and socio-economic sciences.В The reaction network approachВ clearly explains the intimate links between the GompertzВ model and the Verhulst logistic model.В There are shown reversible reactions which complete the already known non-reversible ones. It is also demonstrated that the proposed approach can be applied in oscillating processes and social-science events.В The paper is richly illustrated with numericalВ computations andВ computer simulations performed by algorithmsВ using the computer algebra systemВ  Mathematica.