Attractor Reconstruction of 3D Quadratic Chaotic Flows with Up to Two Nonlinearities Through the Cuckoo Search Algorithm

This paper addresses the problem of recovering the general shape and structure of the attractor of a chaotic flow, known as attractor reconstruction problem. This is a very challenging task, as the chaotic systems exhibit a high sensitivity to initial conditions. In fact, only partial success has been achieved so far, mostly for the discrete case (chaotic maps). In this work, we consider the more difficult case of chaotic flows. In our approach, the attractor reconstruction problem is formulated as an optimization problem. It is however too difficult to be solved in all its generality, so we focus on the case of 3D quadratic chaotic flows with up to two nonlinearities. This task is performed through a popular swarm intelligence technique: the cuckoo search algorithm with Lévy flights. It is applied to the reconstruction of several periodic and chaotic behaviors of chaotic flows. Our results show that we are able to reconstruct the corresponding attractors with reasonably good accuracy.