Cuckoo Search Algorithm with Levy Flights for Reconstruction of Periodic and Chaotic Orbits of the 2D Henon Map

Reconstructing the complex behavior of chaotic dynamical systems from time series is a challenging task, due to the high sensitivity to initial conditions and other factors. In this paper, we formulate this issue as an optimization problem, which is addressed through a bio-inspired swarm intelligence technique: the cuckoo search algorithm with Lévy flights. The method is applied to reconstruct several periodic and chaotic behaviors of the Hénon map, a popular two-dimensional chaotic map. Our graphical and numerical results show that the proposed method is able to obtain suitable values for the parameters under optimization and reconstruct different system behaviors with good accuracy.