On some classes of growth functions and their links to reaction network theory

In this work we study some characteristics of sigmoidal growth functions that are solutions to dynamical systems induced by reaction networks. The studied dynamical systems are close to the Gompertzian and logistic type growth models. Apart from the growing species, the considered reaction networks involve additional decaying species interpreted as environmental resource(s). Using reaction network theory approach, we formulate several modifications/generalizations of the classic logistic Verhulst model, borrowing ideas from the reaction network formulation of the Gompertz model. Our study of the monotonicity order-preservation properties of the model solutions is supported by numerical computations and graphical visualizations. We also attempt a classification of the reaction networks inducing growth-decay models based on the types of the elementary reactions incorporated in these networks.