Sandra Aleixo: An Extension of Gompertzian Growth Dynamics: Weibull and Fréchet Models

V četrtek, 26. maja 2016, ob 14:15 bo v predavalnici 3.06 Fakultete za matematiko in fiziko Univerze v Ljubljani na Jadranski ulici 21 v Ljubljani potekalo predavanje Sandre Aleixo, ISEL, Lizbona, z naslovom An Extension of Gompertzian Growth Dynamics: Weibull and Fréchet Models.

Abstract:   In this seminar I will present a new probabilistic and dynamical approach to an extension of the  Gompertz law.  One  starts  by 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  regions  of regression, stability, bifurcation, chaos and terminus are identified.