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Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Extreming curves and the parameter space of a generalized Logistic mapping

Journal of Vcibration Testing and System Dynamics 2(2) (2018) 109--118 | DOI:10.5890/JVTSD.2018.06.002

Diogo Ricardo da Costa$^{1}$, Matheus Hansen$^{2}$, Edson D. Leonel$^{1}$, Rene O. Medrano-T$^{3}$

$^{1}$ Departamento de Física, UNESP - Univ Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP - Brazil

$^{2}$ Instituto de Física da Universidade de S~ao Paulo, Rua do Matão, Travessa R 187, Cidade Universitária, 05314-970 São Paulo, SP - Brazil

$^{3}$ Departamento de Física, UNIFESP - Universidade Federal de São Paulo, Rua São Nicolau, 210, Centro, 09913-030, Diadema, SP, Brazil

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Abstract

A logistic map with parametric perturbation is studied. We confirm the model exhibits self-similar structures in the parameter space known as shrimps. The organization of such structures may be describe through extreme curves, giving exactly the position of each one of them in a complicated behavior in the parameter space. Boundary crisis are also discussed. They lead to an abrupt destruction of the chaotic attractor and how such destruction affects the dynamics of the system is discussed, particularly affecting the time before the orbit leaves to infinite. By a specific choice of the parameters we show the existence of strange non-chaotic attractors in the parameter space.

Acknowledgments

DRC acknowledges to PNPD/CAPES. MH thanks to CAPES for the nancial support. EDL thanks to CNPq (303707/2015-1), FUNDUNESP and FAPESP (2017/14414-2), Brazilian agencies. RMT thanks to FAPESP (2015/50122-0). This research was supported by resources supplied by the Center for Scientific Computing (NCC/GridUNESP) of the São Paulo State University (UNESP).

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