Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.21/2795
Título: An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models
Autor: Rocha, José Leonel Linhares da
Aleixo, Sandra Maria
Palavras-chave: Growth models
Extreme value laws
Beta* (p, q) densities
Bifurcations and chaos
Symbolic dynamics
Topological entropy
Tumour dynamics
Logistic Model
Data: Abr-2013
Editora: Amer Inst Mathematical Sciences
Citação: ROCHA, J. Leonel; AlLEIXO, Sandra M. - An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models. Mathematical Biosciences and Engineering. ISSN 1547-1063. Vol. 10, nr 2 (2013), p. 379-398.
Resumo: In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.
Peer review: yes
URI: http://hdl.handle.net/10400.21/2795
ISSN: 1547-1063
Aparece nas colecções:ISEL - Matemática - Artigos

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