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<p>In this work, we investigated the behavior of basins of attraction and the nonlinear dynamics of a system of two coupled Van der Pol oscillators considering the action of an external force on one of the oscillators. Thus, we performed the parametric sweep and identified the screening in some basins with the uncertainty exponent and entropy basins of attraction. With these quantities, we were able to observe the possible fractality in the basins of attraction and thus establish the set of parameters that can alter the behavior of the initial conditions that are used in the coupled system. Another analysis was the nonlinear dynamics exploring the parameter space with the maximum Lyapunov exponent and thus establish a diagnosis of the regions that may possibly have chaotic behavior. Such results are confirmed with the phase maps, Poincaré maps, and the bifurcation diagram. These analyses corroborate future work such as the proposal of control techniques for the suppression of chaos in these established regions.</p>

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Comments of Non-linear Numerical Analysis of Van der Pol Oscillator Coupled

  • 期刊论文

  • 发表日期：

    2025年3月31日

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  • Gabriella de O. M. Silva,
  • Mauricio A. Ribeiro,
  • Jeferson J. de Lima,
  • Angelo M. Tusset,
  • Marcus Varanis,
  • Jose M. Balthazar,
  • Clivaldo de Oliveira

摘要

In this work, we investigated the behavior of basins of attraction and the nonlinear dynamics of a system of two coupled Van der Pol oscillators considering the action of an external force on one of the oscillators. Thus, we performed the parametric sweep and identified the screening in some basins with the uncertainty exponent and entropy basins of attraction. With these quantities, we were able to observe the possible fractality in the basins of attraction and thus establish the set of parameters that can alter the behavior of the initial conditions that are used in the coupled system. Another analysis was the nonlinear dynamics exploring the parameter space with the maximum Lyapunov exponent and thus establish a diagnosis of the regions that may possibly have chaotic behavior. Such results are confirmed with the phase maps, Poincaré maps, and the bifurcation diagram. These analyses corroborate future work such as the proposal of control techniques for the suppression of chaos in these established regions.