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- W4320917648 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." @default.
- W4320917648 created "2023-02-16" @default.
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- W4320917648 date "2023-02-15" @default.
- W4320917648 modified "2023-10-18" @default.
- W4320917648 title "Generalized Beta Models and Population Growth: So Many Routes to Chaos" @default.
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- W4320917648 doi "https://doi.org/10.3390/fractalfract7020194" @default.
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