Effects of a parametric perturbation in the Hassell mapping

Author(s)

de Oliveira, Juliano A. ^{[1, 2]} ; de Mendonca, Hans M. J. ^[1] ; da Costa, Diogo R. ^[1] ; Leonel, Edson D. ^{[3, 1]}

Affiliation

^[1] Univ Estadual Paulista UNESP, Inst Geociencias & Ciencias Exatas, Dept Fis, Campus Rio Claro, Av 24A, 1515, BR-13506900 Sao Paulo, SP - Brazil

^[2] Univ Estadual Paulista UNESP, Campus Sao Joao Boa Vista, BR-13876750 Sao Paulo, SP - Brazil

^[3] Abdus Salam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste - Italy

• Document type: Review article
• Source: CHAOS SOLITONS & FRACTALS; v. 113, p. 238-243, AUG 2018.
• Web of Science Citations: 0

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. (C) 2018 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 15/22062-3 - Scaling properties and cascades bifurcations in one-dimensional discrete maps
• Grantee: Hans Muller Junho de Mendonça
• Support Opportunities: Scholarships in Brazil - Master
• FAPESP's process: 14/18672-8 - Effects of dissipation, transient and dynamical properties in discrete mappings
• Grantee: Juliano Antonio de Oliveira
• Support Opportunities: Regular Research Grants
• FAPESP's process: 17/14414-2 - Scaling investigation in dynamical systems
• Grantee: Edson Denis Leonel
• Support Opportunities: Regular Research Grants
• FAPESP's process: 12/23688-5 - Exponents and scaling laws, phase transitions and transport properties of time dependent systems
• Grantee: Edson Denis Leonel
• Support Opportunities: Regular Research Grants