Generalized exponential function and discrete growth models

Autor(es)

Martinez, Alexandre Souto ^[1] ; Gonzalez, Rodrigo Silva ; Espindola, Aquino Lauri ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 388, n. 14, p. 2922-2930, JUL 15 2009.
• Citações Web of Science: 18

Resumo

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)

• Processo FAPESP: 06/60333-0 - Dinâmicas migratórias com modelos computacionais baseados em agentes
• Beneficiário: Aquino Lauri de Espíndola
• Modalidade de apoio: Auxílio à Pesquisa - Programa Primeiros Projetos