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

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  • de Mendonça, Hans M.J.
  • Leonel, Edson D.
  • de Oliveira, Juliano A.

Abstract

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.

Suggested Citation

  • de Mendonça, Hans M.J. & Leonel, Edson D. & de Oliveira, Juliano A., 2017. "An investigation of the convergence to the stationary state in the Hassell mapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 537-543.
    • Handle: RePEc:eee:phsmap:v:466:y:2017:i:c:p:537-543
    DOI: 10.1016/j.physa.2016.09.045
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    1. Costa Júnior, Manoel Pedro da & Khan, Ahmad Saeed & Sousa, Eliane Pinheiro de & Lima, Patrícia Verônica Pinheiro Sales, 2015. "53," Revista de Economia e Sociologia Rural (RESR), Sociedade Brasileira de Economia e Sociologia Rural, vol. 53(2), January.
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