Populational Growth Models Proportional to Beta Densities with Allee Effect

Aleixo, Sandra M.; Rocha, J. Leonel; Pestana, Dínis; Cabada, Alberto; Liz, Eduardo; Nieto, Juan J.

doi:10.1063/1.3142952

Cited by 12 publications

(13 citation statements)

References 2 publications

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“…The generalized logistic models we shall use are proportional to the Beta(p, 2) densities, with p ∈ ]1, +∞[, [2]. This family provides more flexible models to theorize population dynamics when the classical logistic or Verhulst Model fails to provide a good fit.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behaviour on the parameter space: New populational growth models proportional to beta densities

Aleixo

Rocha

Pestana

2009

Proceedings of the ITI 2009 31st International Conference on Information Technology Interfaces

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We present new populational growth models, generalized logistic models which are proportional to beta densities with shape parameters p and 2, where p > 1, with Malthusian parameter r. The complex dynamical behaviour of these models is investigated in the parameter space (r, p), in terms of topological entropy, using explicit methods, when the Malthusian parameter r increases. This parameter space is split into different regions, according to the chaotic behaviour of the models.

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Section: Introductionmentioning

confidence: 99%

Dynamical behaviour on the parameter space: New populational growth models proportional to beta densities

Aleixo

Rocha

Pestana

2009

Proceedings of the ITI 2009 31st International Conference on Information Technology Interfaces

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“…Rocha and al. in [1,5] have shown that there exists a relation between the parameters p, q and c such that for all r ∈]r 1 , r 2 [, we can assure the existence of a unique attractor for x ∈ [0; 1] with…”

Section: Endomorphisms Depending Of Two Parameters (R P)mentioning

confidence: 99%

Attractors and commutation sets in Hénon-like diffeomorphisms

Selmani

Djellit²

2018

B Soc Paran Mat

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In this work we display Hénon-like attractors that emerge and appear in diffeomorphisms generated by embedding of one-dimensional endomorphisms.We show the properties of basin of attraction, and identify various types of attractors and commutation sets which are associated with these diffeomorphisms. Numerically presented scenarii of the creation and destruction of these attractors via bifurcations are illustrated.

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“…In previous studies, the authors presented a successful approach to study population growth models, proportional to Beta(p, 2) densities, [1] and [2]. These models are natural extensions of the logistic Verhuslt growth model, originally introduced as a demographic model and often considered as the basis of modern chaos theory.…”

Section: Introductionmentioning

confidence: 99%

“…In [6], we generalized these models by adding a positive parameter C, which allows models to be more flexible with variable extinction rates. The case of C = 0 was studied in [2].…”

Section: Introductionmentioning

confidence: 99%

“…These models are natural extensions of the logistic Verhuslt growth model, originally introduced as a demographic model and often considered as the basis of modern chaos theory. The models presented have no Allee effect for some values of the parameter p, namely for 1 < p ≤ 2, but this drawback was corrected since the authors suggested suitable corrections, [2]. In [6], we generalized these models by adding a positive parameter C, which allows models to be more flexible with variable extinction rates.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Models from Beta(p, 2) Densities with Strong Allee Effect: Dynamical Approach

Aleixo

Rocha

2012

CIT

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A dynamical approach to study the behaviour of generalized populational growth models from Beta(p, 2) densities, with strong Allee effect, is presented. The dynamical analysis of the respective unimodal maps is performed using symbolic dynamics techniques. The complexity of the correspondent discrete dynamical systems is measured in terms of topological entropy. Different populational dynamics regimes are obtained when the intrinsic growth rates are modified: extinction, bistability, chaotic semistability and essential extinction.

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Populational Growth Models Proportional to Beta Densities with Allee Effect

Cited by 12 publications

References 2 publications

Dynamical behaviour on the parameter space: New populational growth models proportional to beta densities

Dynamical behaviour on the parameter space: New populational growth models proportional to beta densities

Attractors and commutation sets in Hénon-like diffeomorphisms

Generalized Models from Beta(p, 2) Densities with Strong Allee Effect: Dynamical Approach

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