Generalized beta models and population growth: so many routes to chaos

M. Fátima Brilhante, M. Ivette Gomes*, Sandra Mendonça, Dinis Pestana, Pedro Pestana

*Autor correspondente para este trabalho

Resultado de pesquisarevisão de pares

39 Transferências (Pure)

Resumo

Logistic and Gompertz growth equations are the usual choice to model sustainable growth and immoderate growth causing depletion of resources, respectively. Observing that the logistic distribution is geo-max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, we investigate other models proportional to either geo-max-stable distributions (log-logistic and backward log-logistic) or to other max-stable distributions (Fréchet or max-Weibull). We show that the former arise when in the hyper-logistic Blumberg equation, connected to the Beta (Formula presented.) function, we use fractional exponents (Formula presented.) and (Formula presented.), and the latter when in the hyper-Gompertz-Turner equation, the exponents of the logarithmic factor are real and eventually fractional. The use of a BetaBoop function establishes interesting connections to Probability Theory, Riemann–Liouville’s fractional integrals, higher-order monotonicity and convexity and generalized unimodality, and the logistic map paradigm inspires the investigation of the dynamics of the hyper-logistic and hyper-Gompertz maps.

Idioma originalEnglish
Número do artigo194
Número de páginas40
RevistaFractal and Fractional
Volume7
Número de emissão2
DOIs
Estado da publicaçãoPublicado - 15 fev. 2023

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