Scaling properties and cascades bifurcations in one-dimensional discrete maps

• Grant number: 15/22062-3
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2016
• End date: February 28, 2018
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Juliano Antonio de Oliveira
• Grantee: Hans Muller Junho de Mendonça
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

In this work we consider a family of one-dimensional discrete maps parameterized by an exponent $\gamma$ as a dynamical variable. The choice of $\gamma=2$ recovers the Gauss map that belongs to class of one-dimensional maps and is a model for the dynamics of biological populations. Defined the mapping, as the control parameter can be varied, bifurcations in fixed points can be observed. We propose to build the orbit diagrams for different values of $\gamma$ to analyze the behavior of the dynamic. We intend to investigate analytically and numerically the decay of orbits for the fixed points and characterize the decay by a homogeneous function. We intend observe if the decay it is universal for different values of the control parameters. In addition, we intend to investigate the relaxation orbits for thebifurcation points and characterize the chaos using the Lyapunov exponents. This research is linked to the project ``Dissipation effects, transient and dynamic properties in discrete mappings'' approved by FAPESP in the process 2014/18672-8.

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DE OLIVEIRA, JULIANO A.; DE MENDONCA, HANS M. J.; DA SILVA, ANDERSON A. A.; LEONEL, EDSON D.. Critical Slowing Down at a Fold and a Period Doubling Bifurcations for a Gauss Map. Brazilian Journal of Physics, v. 49, n. 6, p. 923-927, DEC 2019. (18/14685-9, 15/22062-3, 14/18672-8, 17/14414-2, 12/23688-5)

DE OLIVEIRA, JULIANO A.; DE MENDONCA, HANS M. J.; FAVARIM, VITOR A.; DE CARVALHO, R. EGYDIO; LEONEL, EDSON D.. Boundary crises and supertrack orbits in the Gauss map. European Physical Journal-Special Topics, v. 231, n. 3, p. 4-pg., 2022-01-25. (21/09519-5, 12/23688-5, 19/07329-4, 18/14685-9, 15/22062-3, 19/14038-6)

DE OLIVEIRA, JULIANO A.; DE MENDONCA, HANS M. J.; DA COSTA, DIOGO R.; LEONEL, EDSON D.. Effects of a parametric perturbation in the Hassell mapping. CHAOS SOLITONS & FRACTALS, v. 113, p. 238-243, AUG 2018. (15/22062-3, 14/18672-8, 17/14414-2, 12/23688-5)

DE MENDONCA, HANS M. J.; LEONEL, EDSON D.; DE OLIVEIRA, JULIANO A.. An investigation of the convergence to the stationary state in the Hassell mapping. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 466, p. 537-543, JAN 15 2017. (14/18672-8, 12/23688-5, 15/22062-3)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MENDONÇA, Hans Muller Junho de. Scaling properties and bifurcation cascades in one-dimensional discrete maps. 2018. Master's Dissertation - Universidade Estadual Paulista (Unesp). Instituto de Geociências e Ciências Exatas. Rio Claro Rio Claro.