Sandra Aleixo
Instituto Superior de Engenharia de Lisboa

In this seminar it will be presented a new probabilistic and dynamical approach to an extension of the Gompertz law. One starts by the introducing 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. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Fréchet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It will be shown how the dynamical analysis is performed using techniques of symbolic dynamics and how the system complexity is measured using the 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.