Abstract
This communication presents a discussion of some extensions of the formalism of Verhulst's simple logistics, which may constitute an autonomous growth model of a more general scope.
For that purpose, the basis concept of growth diagram or trajectory is called upon, as it affords the graphic representation of the change in the growth variable y, using two relevant kinetic parameters: the instantaneous rate and the instantaneous acceleration. The two possible kinds of trajectories are in relation to the use of absolute (V = dyldt; Γ = dV/dt) or relative (or specific) values (R = (1/y)(dy/dt); Γ R = dR/dt).
In the case of simple logistics, the trajectory (V, Γ) allows 4 growth phases or states to be distinguished. The diagram (R, Γ R ) shows that the deceleration of the specific rate is not monotonous.
In the case of Richards - Nelder's generalized logistics, the qualitative variation of the growth trajectory depends on the value of the dissymmetry parameter (occurrence of a critical value which determines the number of growth states).
Blumberg's model is characterized by an analogous property and, moreover, can account for a non monotonous variation of the specific growth rate.
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Buis, R. On the generalization of the logistic law of growth. Acta Biotheor 39, 185–195 (1991). https://doi.org/10.1007/BF00114174
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DOI: https://doi.org/10.1007/BF00114174