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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Generalized exponential function and discrete growth models

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Author(s):
Martinez, Alexandre Souto [1] ; Gonzalez, Rodrigo Silva ; Espindola, Aquino Lauri [2]
Total Authors: 3
Affiliation:
[1] Natl Inst Sci & Technol Complex Syst, BR-14040901 Sao Paulo - Brazil
[2] Univ Sao Paulo, Fac Filosofia Ciencias & Letras Ribeirao Preto, Dept Fis & Matemat, BR-14040901 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 388, n. 14, p. 2922-2930, JUL 15 2009.
Web of Science Citations: 18
Abstract

Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards' model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) theta-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized theta-Ricker model one is able to retrieve either scramble or contest models. (C) 2009 Elsevier B.V. All rights reserved. (AU)