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Effects of a parametric perturbation in the Hassell mapping

Author

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  • de Oliveira, Juliano A.
  • de Mendonça, Hans M.J.
  • da Costa, Diogo R.
  • Leonel, Edson D.

Abstract

The convergence to the fixed point near at a transcritical bifurcation and the organization of the extreming curves for a parametric perturbed Hassell mapping are investigated. The evolution of the orbits towards the fixed point at the transcritical bifurcation is described using a phenomenological approach with the support of scaling hypotheses and homogeneous function hence leading to a scaling law related with three critical exponents. Near the bifurcation the decay to the fixed point is exponential with a relaxation time given by a power law. The extreming curves in the parameter space dictates the organization for the windows of periodicity, consequently demonstrating how the set of shrimp-like structures are organized.

Suggested Citation

  • de Oliveira, Juliano A. & de Mendonça, Hans M.J. & da Costa, Diogo R. & Leonel, Edson D., 2018. "Effects of a parametric perturbation in the Hassell mapping," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 238-243.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:238-243
    DOI: 10.1016/j.chaos.2018.06.017
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    References listed on IDEAS

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    1. Oded Galor, 2007. "Discrete Dynamical Systems," Springer Books, Springer, edition 1, number 978-3-540-36776-5, June.
    2. 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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    Cited by:

    1. da Costa, Diogo Ricardo & Rocha, Julia G.S. & de Paiva, Luam S. & Medrano-T, Rene O., 2021. "Logistic-like and Gauss coupled maps: The born of period-adding cascades," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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