Stabilization of Higher Periodic Orbits of the Lozi and Hénon Maps using Meta-evolutionary Approaches

摘要

This paper deals with an advanced adjustment of stabilization sequences for selected discrete chaotic systems by means of meta-evolutionary approaches. As the representative models of deterministic chaotic systems, a two dimensional Lozi map and two dimensional Hénon map were used. The novelty of the approach is in an effective use of a new type of objective function, which is essential for the whole optimization process of higher periodic orbits as well as an effective use of advanced metaheuristic optimization methods. Although the task of stabilizing the Lozi and Hénon chaotic systems is known, its solution presented for periodic orbit four is not trivial. The task of stabilizing the Lozi chaotic systems for period four is a new approach. Furthermore, modern meta-heuristics were used for own design of the external disturbance sequences. The used optimization methods are a naive grid-based algorithm (NG), a grid-based Nelder-Mead Algorithm (NM), a Genetic Algorithm (GA) as well as Genetic Programming (GP). A connection of GP and second level optimization using GA displays significantly better results than the given stand-alone meta-heuristic techniques.