An investigation of the convergence to the stationary state in the Hassell mapping

We investigate the convergence to the fixed point and near it in a transcritical bifurcation observed in a Hassell mapping. We considered a phenomenological description which was reinforced by a theoretical description. At the bifurcation, we confirm the convergence for the fixed point is characteri...

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Bibliographic Details
Published inPhysica A Vol. 466; pp. 537 - 543
Main Authors de Mendonça, Hans M.J., Leonel, Edson D., de Oliveira, Juliano A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.01.2017
Subjects
Bifurcations
Hassell map
Scaling law
Scaling law
Bifurcations
Hassell map
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Summary:We investigate the convergence to the fixed point and near it in a transcritical bifurcation observed in a Hassell mapping. We considered a phenomenological description which was reinforced by a theoretical description. At the bifurcation, we confirm the convergence for the fixed point is characterized by a homogeneous function with three exponents. Near the bifurcation the decay to the fixed point is exponential with a relaxation time given by a power law. Although the expression of the mapping is different from the traditional logistic mapping, at the bifurcation and near it, the local dynamics is essentially the same for either mappings.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2016.09.045