| An extension of Gompertzian growth dynamics: Weibull and Frechet models. | |
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MedLine Citation:
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PMID: 23458306 Owner: NLM Status: In-Data-Review |
Abstract/OtherAbstract:
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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. |
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Authors:
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J Leonel Rocha; Sandra M Aleixo |
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Publication Detail:
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Type: Journal Article |
Journal Detail:
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Title: Mathematical biosciences and engineering : MBE Volume: 10 ISSN: 1551-0018 ISO Abbreviation: Math Biosci Eng Publication Date: 2013 Apr |
Date Detail:
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Created Date: 2013-03-05 Completed Date: - Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 101197794 Medline TA: Math Biosci Eng Country: United States |
Other Details:
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Languages: eng Pagination: 379-98 Citation Subset: IM |
Affiliation:
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Instituto Superior de Engenharia de Lisboa - ISEL, ADM and CEAUL, Rua Conselheiro Emidio Navarro, 1, 1959-007 Lisboa, Portugal. jrocha@adm.isel.pt. |
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