Publicação
Generalized beta models and population growth: so many routes to chaos
| dc.contributor.author | Brilhante, M. Fátima | |
| dc.contributor.author | Gomes, M. Ivette | |
| dc.contributor.author | Mendonça, Sandra | |
| dc.contributor.author | Pestana, Dinis | |
| dc.contributor.author | Pestana, Pedro | |
| dc.date.accessioned | 2023-03-28T17:51:46Z | |
| dc.date.available | 2023-03-28T17:51:46Z | |
| dc.date.issued | 2023-02-15 | |
| 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 (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. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.doi | 10.3390/fractalfract7020194 | pt_PT |
| dc.identifier.eid | 85148911001 | |
| dc.identifier.issn | 2504-3110 | |
| dc.identifier.uri | http://hdl.handle.net/10400.14/40736 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
| dc.subject | Beta and BetaBoop | pt_PT |
| dc.subject | Extreme and geo-extreme distributions | pt_PT |
| dc.subject | Fractional calculus | pt_PT |
| dc.subject | Generalized convexity and unimodality | pt_PT |
| dc.subject | Hyper-logistic and hyper-Gompertz growth | pt_PT |
| dc.subject | Nonlinear maps | pt_PT |
| dc.title | Generalized beta models and population growth: so many routes to chaos | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.issue | 2 | pt_PT |
| oaire.citation.title | Fractal and Fractional | pt_PT |
| oaire.citation.volume | 7 | pt_PT |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |