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[A contribution to the generalization of the Gompertz function]
Gegenbaurs Morphologisches Jahrbuch
|January 1, 1979
Summary
This study redefines the Gompertz function by establishing that its logarithmic derivation of relative growth rate is constant. Extensions to this model allow for a broader range of growth functions applicable in various scientific fields.
Area of Science:
- Mathematical Biology
- Growth Modeling
Context:
- The Gompertz function is a widely used model for describing growth patterns in biological and economic systems.
- Existing literature presents differing differential equations for the Gompertz function, necessitating clarification and unification.
Purpose:
- To mathematically clarify and unify the differential equations associated with the Gompertz growth function.
- To propose a generalized definition of the Gompertz function based on the logarithmic derivation of its relative growth rate.
- To explore extensions of the Gompertz function by considering time-dependent parameters.
Summary:
- The study demonstrates that a key property defining the Gompertz function is a constant logarithmic derivation of the relative growth rate.
- It mathematically proves that a specific differential equation (Eq. 2) is a special case, while a more general form applies.
- By allowing the parameter 'c' to be a function of time, the Gompertz model is extended, yielding a family of new growth functions.
Impact:
- Provides a more robust and general mathematical foundation for the Gompertz growth model.
- Enables the development of novel, model-based extensions of the Gompertz function for enhanced applicability.
- Facilitates more accurate and flexible modeling of diverse growth phenomena across scientific disciplines.