Continuous growth models in terms of generalized logarithm and exponential functions

TL;DR

This paper explores generalized logarithm and exponential functions derived from hyperboles, demonstrating their effectiveness in unifying continuous growth models and providing physical insights, especially for Richards' model.

Contribution

It introduces a unified framework for continuous growth models using generalized functions and offers a physical interpretation for the model parameter.

Findings

Generalized functions effectively describe various growth models.

Unified approach simplifies understanding of growth dynamics.

Physical interpretation enhances model applicability.

Abstract

Consider the one-parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non-symmetrical hyperboles. These generalizations coincide to the one obtained in the context of non-extensive thermostatistics. We show that these functions are suitable to describe and unify the great majority of continuous growth models, which we briefly review. Physical interpretation to the generalization function parameter is given for the Richards' model, which has an underlying microscopic model to justify it.