Effects of a parametric perturbation in the Hassell mapping

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.