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Advisor(s)
Abstract(s)
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.
Description
Keywords
Growth models Extreme value laws Beta* (p, q) densities Bifurcations and chaos Symbolic dynamics Topological entropy Tumour dynamics Logistic Model Tumor-Growth Immunotherapy
Citation
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.