|Autors: Lazarova, M. D., Markov S., Vassilev A.|
Title: On some classes of growth functions and their links to eaction network theory
Keywords: reaction networks, growth functions, growth-decay models
Abstract: 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 Gompertzian and logistic type growth models. Apart from the growing species, the considered reaction network involve additional decaying species interpreted as environmental resources. Using reaction network theory approach, we formulate several modifications/generalizations of the classical logistic Verhulst model, borrowing ideas from the reaction network formulation of 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 including growth-decay models based on the types of the elementary reactions incorporated in these networks.
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