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Von Bertalanffy's growth dynamics with strong Allee effect

J. Leonel RochaSandra M. Aleixo — 2012

Discussiones Mathematicae Probability and Statistics

Von Bertalanffy’s model is one of the most popular differential equation used in order to study the increase in average length or weight of fish. However, this model does not include demographic Allee effect. This phenomenon is known in the fisheries literature as “depensation”, which arises when populations decline rapidly at low densities. In this paper we develop and investigate new corrected von Bertalanffy’s models with Allee effects. The generalization that we propose results from considering...

The Beta(p,1) extensions of the random (uniform) Cantor sets

Dinis D. PestanaSandra M. AleixoJ. Leonel Rocha — 2009

Discussiones Mathematicae Probability and Statistics

Starting from the random extension of the Cantor middle set in [0,1], by iteratively removing the central uniform spacing from the intervals remaining in the previous step, we define random Beta(p,1)-Cantor sets, and compute their Hausdorff dimension. Next we define a deterministic counterpart, by iteratively removing the expected value of the spacing defined by the appropriate Beta(p,1) order statistics. We investigate the reasons why the Hausdorff dimension of this deterministic fractal is greater...

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