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

Abstract

We investigate the behavior of basins of attraction and the nonlin- ear 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 phenom- ena. 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 Poincar´e maps with their respective initial conditions. Such analyses corroborate future work involving control design to suppress chaotic behavior. ©2025 L&H Scientific Publishing, LLC. All rights reserved.