Cuckoo Search Algorithm for Chaos Control of Two-Dimensional Chaotic Maps
摘要
Chaotic systems exhibit extreme sensitivity to initial conditions, where even slight differences on the initial conditions can cause trajectories to diverge over time. Since the 1990s, researchers have demonstrated that chaotic behavior can be controlled – a phenomenon known as chaos control. In this context, this work focuses on stabilizing chaotic dynamics in two-dimensional maps by steering them toward a periodic orbit of a specified period. Our approach builds on a previous method that applies pulses of intensity \(\lambda \) to the system variables every \(\Delta n\) iterations, where \(\lambda \) and \(\Delta n\) are method parameters. We formulate this problem as a complex, multimodal, multivariate, continuous nonlinear optimization task, tackled using a popular swarm intelligence technique called cuckoo search algorithm. Computational experiments on the Holmes map under various parameter settings demonstrate that our method performs effectively, representing a promising step toward fully automated chaos control in chaotic maps.