Effects of a parametric perturbation in the Hassell mapping

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de Oliveira, Juliano A. [UNESP]
de Mendonça, Hans M.J. [UNESP]
da Costa, Diogo R. [UNESP]
Leonel, Edson D. [UNESP]
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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.
Convergence to the stationary state, Extreming curves, Parameter space, Perturbed Hassell mapping
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Chaos, Solitons and Fractals, v. 113, p. 238-243.