Publication
Generalized beta models and population growth: so many routes to chaos
| datacite.subject.fos | Ciências Naturais::Matemáticas | |
| dc.contributor.author | Brilhante, Maria de Fátima | |
| dc.contributor.author | Gomes, Maria Ivette | |
| dc.contributor.author | Mendonça, Sandra | |
| dc.contributor.author | Pestana, Dinis | |
| dc.contributor.author | Pestana, Pedro Duarte | |
| dc.date.accessioned | 2026-01-08T14:47:15Z | |
| dc.date.available | 2026-01-08T14:47:15Z | |
| dc.date.issued | 2023-01 | |
| dc.description.abstract | 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 (p, q) function, we use fractional exponents p − 1 = 1 ∓ 1/α and q − 1 = 1 ± 1/α, 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. | eng |
| dc.identifier.citation | Brilhante, M.F., Gomes, M.I., Mendonça, S., Pestana, D. & Pestana, P.D. (2023). Generalized Beta Models and Population Growth: So Many Routes to Chaos. Fractal and Fractional. 7, 2, 40 p., 194. | |
| dc.identifier.doi | 10.3390/fractalfract7020194 | |
| dc.identifier.issn | 2504-3110 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/20707 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | MDPI | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Beta and BetaBoop | |
| dc.subject | Fractional Calculus | |
| dc.subject | Nonlinear Maps | |
| dc.title | Generalized beta models and population growth: so many routes to chaos | eng |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.issue | 2 | |
| oaire.citation.title | Fractal and Fraccional | |
| oaire.citation.volume | 7 | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |
| person.affiliation.name | Universidade Aberta | |
| person.familyName | Pestana | |
| person.givenName | Pedro Duarte | |
| person.identifier.ciencia-id | 2714-8A7B-5CCA | |
| person.identifier.orcid | 0000-0002-3406-1077 | |
| person.identifier.rid | E-7273-2016 | |
| person.identifier.scopus-author-id | 56074016300 | |
| relation.isAuthorOfPublication | 755592cd-7905-4c94-9eba-1bb83ce10355 | |
| relation.isAuthorOfPublication.latestForDiscovery | 755592cd-7905-4c94-9eba-1bb83ce10355 |