Effects of dissipation, transient and dynamical properties in discrete mappings

• Grant number: 14/18672-8
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2014
• End date: October 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Juliano Antonio de Oliveira
• Grantee: Juliano Antonio de Oliveira
• Host Institution: Universidade Estadual Paulista (UNESP). Campus Experimental São João da Boa Vista. São João da Boa Vista , SP, Brazil
• Associated researchers: Edson Denis Leonel

Abstract

In this project we consider a family of one-dimensional mappings parametrised by a exponent $\gamma$ as a dynamical variable. Choosing some control parameters and a transformation in the spatial variable we recover different mappings known in the literature. We propose in this research to build orbit diagrams to analyse the dynamics of the system.We intend to study analytically and numerically the convergence to fixed points and use Lyapunov exponents to characterize the chaos. We propose extend our studies to analyse the family of two-dimensional mappings parametrized by control parameter $\gamma$. We propose introduce dissipation in the system to investigate the crisis boundary phenomena and analyse the space parameters. We restrict to the study of the Fermi-Ulam model under a action of external force. The main goals in this study is investigate analytically the average properties along of chaotic orbits to found critical expoenents to define universality classes. (AU)

Scientific publications

(11)

(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)

MENDEZ-BERMUDEZ, J. A.; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D.. Two-dimensional nonlinear map characterized by tunable Levy flights. Physical Review E, v. 90, n. 4, OCT 27 2014. (13/14655-9, 14/18672-8, 12/23688-5)

DE OLIVEIRA, JULIANO A.; MONTERO, LEONARDO T.; DA COSTA, DIOGO R.; MENDEZ-BERMUDEZ, J. A.; MEDRANO-T, RENE O.; LEONEL, EDSON D.. An investigation of the parameter space for a family of dissipative mappings. Chaos, v. 29, n. 5, MAY 2019. (14/18672-8, 18/14685-9, 17/14414-2, 15/50122-0)

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 OLIVEIRA, JULIANO A.; RAMOS, LARISSA C. N.; LEONEL, EDSON D.. Dynamics towards the steady state applied for the Smith-Slatkin mapping. CHAOS SOLITONS & FRACTALS, v. 108, p. 119-122, MAR 2018. (17/14414-2, 17/17294-8, 14/18672-8)

PERRE, RODRIGO M.; CARNEIRO, BARBARA P.; MENDEZ-BERMUDEZ, J. A.; LEONEL, EDSON D.; DE OLIVEIRA, JULIANO A.. On the dynamics of two-dimensional dissipative discontinuous maps. CHAOS SOLITONS & FRACTALS, v. 131, FEB 2020. (18/14685-9, 17/14414-2, 19/06931-2, 14/18672-8)

MENDEZ-BERMUDEZ, J. A.; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D.. Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps. Physics Letters A, v. 380, n. 22-23, p. 1959-1963, MAY 20 2016. (12/23688-5, 14/25997-0, 13/14655-9, 14/18672-8)

MENDEZ-BERMUDEZ, J. A.; DE OLIVEIRA, JULIANO A.; AGUILAR-SANCHEZ, R.; LEONEL, EDSON D.. Scaling properties for a family of discontinuous mappings. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 436, p. 943-951, OCT 15 2015. (12/23688-5, 14/25997-0, 13/14655-9, 14/18672-8)

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)

DA COSTA, DIOGO RICARDO; DETTMANN, CARL P.; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D.. Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism. Chaos, v. 25, n. 3, MAR 2015. (12/23688-5, 14/18672-8, 12/18962-0, 13/22764-2)

MENDEZ-BERMUDEZ, J. A.; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D.. Two-dimensional nonlinear map characterized by tunable Levy flights. Physical Review E, v. 90, n. 4, p. 5-pg., 2014-10-27. (12/23688-5, 13/14655-9, 14/18672-8)