Stabilization of Higher Periodic Orbits of the Duffing Map using Meta-evolutionary Approaches: A Preliminary Study
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- @InProceedings{Matousek:2022:CEC,
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author = "Radomil Matousek and Tomas Hulka",
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title = "Stabilization of Higher Periodic Orbits of the Duffing
Map using Meta-evolutionary Approaches: A Preliminary
Study",
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booktitle = "2022 IEEE Congress on Evolutionary Computation (CEC)",
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year = "2022",
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editor = "Carlos A. Coello Coello and Sanaz Mostaghim",
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address = "Padua, Italy",
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month = "18-23 " # jul,
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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",
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isbn13 = "978-1-6654-6708-7",
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DOI = "doi:10.1109/CEC55065.2022.9870372",
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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.",
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notes = "Also known as \cite{9870372}",
- }
Genetic Programming entries for
Radomil Matousek
Tomas Hulka
Citations