Chaotic systems are characterized by extreme sensitivity to initial conditions, where two arbitrarily close starting points lead to exponentially divergent trajectories over time. Since the 1990s, research has demonstrated that chaotic behavior can be controlled, a phenomenon known as chaos control. In this paper, we address the problem of chaos control in unidimensional maps, specifically focusing on stabilizing chaotic dynamics to a periodic orbit of a given period. Our approach builds on a previously proposed method that applies control pulses of intensity \(\lambda \) to the system variables every \(\varDelta n\) iterations, where \(\lambda \) and \(\varDelta n\) are adjustable parameters. We formulate this problem as a challenging multimodal, multivariate, continuous, nonlinear optimization task and tackle it using the bat algorithm, a popular swarm intelligence method. To evaluate the effectiveness of our approach, we conduct computational experiments on the logistic map under various parameter settings. The results indicate that our method performs effectively for all tested chaotic behaviors. We conclude that the proposed approach is a promising step toward an automated procedure for chaos control in chaotic maps.

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Bat Algorithm for Automatic Chaos Control Method Driven by Multiplicative Pulses to the System Variables on the Logistic Map

  • Akemi Gálvez,
  • Andrés Iglesias

摘要

Chaotic systems are characterized by extreme sensitivity to initial conditions, where two arbitrarily close starting points lead to exponentially divergent trajectories over time. Since the 1990s, research has demonstrated that chaotic behavior can be controlled, a phenomenon known as chaos control. In this paper, we address the problem of chaos control in unidimensional maps, specifically focusing on stabilizing chaotic dynamics to a periodic orbit of a given period. Our approach builds on a previously proposed method that applies control pulses of intensity \(\lambda \) to the system variables every \(\varDelta n\) iterations, where \(\lambda \) and \(\varDelta n\) are adjustable parameters. We formulate this problem as a challenging multimodal, multivariate, continuous, nonlinear optimization task and tackle it using the bat algorithm, a popular swarm intelligence method. To evaluate the effectiveness of our approach, we conduct computational experiments on the logistic map under various parameter settings. The results indicate that our method performs effectively for all tested chaotic behaviors. We conclude that the proposed approach is a promising step toward an automated procedure for chaos control in chaotic maps.