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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

Remarks on the Numerical Analysis of Basins of Attraction using Complex Variables

Journal of Vibration Testing and System Dynamics 9(2) (2025) 179--186 | DOI:10.5890/JVTSD.2025.06.008

Mauricio A. Ribeiro$^1$, Pamela Rafaela Martins$^2$, Daniel Felipe Meurer$^{3}$, Hilson Henrique Daum$^1$, Ângelo M. Tusset$^1$, Jose Manoel Balthazar$^{1,4}$

$^1$ Department of Electrical, UTFPR, Campus Ponta Grossa

$^2$ Department of Physics, PUC, Campus Curitiba

$^3$ Centro Universitário FAVENI, Campus Curitiba

$^4$ Mechanical Faculty, UNESP, Campus Bauru

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Abstract

We investigate the behavior of basins of attraction and the nonlinear dynamics of an oscillator described in complex variables. To do this, we analyze the basin entropy and the uncertainty coefficient, establishing whether the attraction basins have the sieve phenomena. Another analysis carried out was with the Lyapunov exponent, which described the chaotic regions in which the oscillator is present. Thus, we were able to diagnose the behavior of the trajectories in phase space. As a result, we determined the set of parameters for Poincaré maps with their respective initial conditions. Such analyses corroborate future work involving control design to suppress chaotic behavior.

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