title: An extension of Gompertzian growth dynamics: Weibull and Frechet models.
abstract: 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.
authors: Instituto Superior de Engenharia de Lisboa - ISEL, ADM and CEAUL, Rua Conselheiro Emidio Navarro, 1, 1959-007 Lisboa, Portugal. jrocha@adm.isel.pt
authors: J Leonel
authors: JL
authors: Rocha
authors: Sandra M
authors: SM
authors: Aleixo
mesh_terms: D000818:Animals; D003198:Computer Simulation; D006128:Growth / Q000502:physiology*; D006801:Humans; D015233:Models, Statistical; D011158:Population Growth