Brilhante, Maria de FátimaGomes, Maria IvetteMendonça, SandraPestana, DinisPestana, Pedro Duarte2026-01-082026-01-082023-01Brilhante, 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., 194.2504-3110http://hdl.handle.net/10400.2/20707Logistic 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.engBeta and BetaBoopFractional CalculusNonlinear Mapsjournal article10.3390/fractalfract7020194