On the generalization of the logistic law of growth

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 = dy/dt; r = dV/dt) or relative (or specific) values (R = (1/y)(dy/dt); r R = dR/dt).In the case of simple logistics, the trajectory (V, I') allows 4 growth phases or states to be distinguished. The diagram (R, re.) shows that the deceleration of the specific rate is not monotonous.In the ease 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.

Global Attractivity of a Generalized Lotka–Volterra Competition Model

“…Model (3) has been studied from different aspects by many researchers. To name a few, see [2,13,19,20]. The data in their experiments show that θ i < 1 and the system admits a unique positive equilibrium.…”

“…We mention that system (8) includes (2) and the often studied models with discrete delay and finite distributed delay of the formsẋ…”

“…Here r i is the intrinsic rate of growth of species i, K i is the carrying capacity of species i, θ i provides a nonlinear measure of intraspecific interference, and α i j provides a measure of interspecific interference, i, j = 1, 2. The model (2) can be regarded as basing on the generalized logistic equation,…”

Caracterisation de la structure d'un processus de croissance

“…The growth kinetics is then characterized by the properties of eseh of phases (71 to G4, with boundaries defined by the singular points Fm~x, Vma x and Fmi n (Buis, 1991(Buis, , 1993. Two types of processes, termed mono-and multi-logistic, can be distinguished.…”

“…The growth kinetics is then characterized by the properties of eseh of phases (71 to G4, with boundaries defined by the singular points Fm~x, Vma x and Fmi n (Buis, 1991(Buis, , 1993. The growth kinetics is then characterized by the properties of eseh of phases (71 to G4, with boundaries defined by the singular points Fm~x, Vma x and Fmi n (Buis, 1991(Buis, , 1993.…”