Stabilization of Higher Periodic Orbits of the Duffing Map using Meta-evolutionary Approaches: A Preliminary Study

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@InProceedings{Matousek:2022:CEC,

• author = "Radomil Matousek and Tomas Hulka",
• title = "Stabilization of Higher Periodic Orbits of the Duffing Map using Meta-evolutionary Approaches: A Preliminary Study",
• booktitle = "2022 IEEE Congress on Evolutionary Computation (CEC)",
• year = "2022",
• editor = "Carlos A. Coello Coello and Sanaz Mostaghim",
• address = "Padua, Italy",
• month = "18-23 " # jul,
• keywords = "genetic algorithms, genetic programming, Chaos, Perturbation methods, Simulation, Metaheuristics, Time series analysis, Linear programming, Chaos control, Evolutionary computation, Nelder-Mead Algorithm, Duffing map, Optimization",
• isbn13 = "978-1-6654-6708-7",
• DOI = "doi:10.1109/CEC55065.2022.9870372",
• abstract = "This paper deals with an advanced adjustment of stabilization sequences for complex chaotic systems by means of meta-evolutionary approaches in the form of a preliminary study. In this study, a two dimensional discrete time dynamic system denoted as Duffing map, also called Holmes map, was used. In general, the Duffing oscillator model represents a real system in the field of nonlinear dynamics. For example, an excited model of a string choosing between two magnets. There are many articles on the stabilization of various chaotic maps, but attempts to stabilize the Duffing map, moreover, for higher orbits, are rather the exception. In the case of period four, this is a novelty. This paper presents several approaches to obtaining stabilizing perturbation sequences. The problem of stabilizing the Duffing map turns out to be difficult and is a good challenge for metaheuristic algorithms, and also as benchmark function. The first approach is the optimal parametrisation of the ETDAS model using multi-restart Nelder-Mead (NM) algorithm and Genetic Algorithm (GA). The second approach is to use the symbolic regression procedure. A perturbation model is obtained using Genetic Programming (GP). The third approach is two level optimization, where the best GP model is subsequently optimized using NM and GA algorithms. A novelty of the approach is also the effective use of the objective function, precisely in relation to the process of optimization of higher periodic paths.",
• notes = "Also known as \cite{9870372}",

}

Genetic Programming entries for Radomil Matousek Tomas Hulka

Citations