Evolutionary identification of hidden chaotic attractors

Abstract

In this participation we discuss the possibility of mutual fusion of evolutionary algorithms and deterministic chaos. As demonstrated in previous research papers, evolutionary algorithms are capable of chaotic system control, identification or synthesis and vice versa, chaos can be observed in the evolutionary dynamics. More exactly, in this paper there is numerically demonstrated possible solution of the question whether identification of so-called basin of attraction for hidden attractor can be done by evolutionary algorithms. Hidden attractors are a special kind of attractors, that are hidden in the system structure and if ignored (undiscovered), then can cause serious damages, as already observed in the real world. The research presented here is bivalent. At first it shows, that evolutionary algorithms are able to identify presence of hidden attractors in the system, but also it can be extended to study an existence of hidden attractors in the evolutionary algorithms dynamics. All numerical simulations are demonstrated on Chua׳s chaotic attractor that contains an example of hidden attractor and at the end there are discussed discrete systems (synthesized by evolution) that likely exhibit hidden attractors, too.