Semi-Stable Periodic Orbits of the Deterministic Chaotic Systems Designed by means of Genetic Programming
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- @InProceedings{matousek:2024:CEC,
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author = "Radomil Matousek and Tomas Hulka and
Rene Pierre Lozi and Jakub Kudela",
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title = "Semi-Stable Periodic Orbits of the Deterministic
Chaotic Systems Designed by means of Genetic
Programming",
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booktitle = "2024 IEEE Congress on Evolutionary Computation (CEC)",
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year = "2024",
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editor = "Bing Xue",
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address = "Yokohama, Japan",
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month = "30 " # jun # " - 5 " # jul,
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publisher = "IEEE",
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keywords = "genetic algorithms, genetic programming, Perturbation
methods, Evolutionary computation, Predictive models,
Linear programming, Orbits, Trajectory, Chaos control,
Periodic orbit, Optimization, Semi-stable",
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isbn13 = "979-8-3503-0837-2",
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DOI = "doi:10.1109/CEC60901.2024.10611935",
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abstract = "The aim of this paper is to show the possibility of
generating general semi-stable periodic orbits using
genetic programming (GP). This concept is a GP design
of a perturbation sequence that forces a defined
dynamical system to behave periodically. Recall that
periodic orbits in deterministic chaotic systems are
trajectories along which the system moves at regular
intervals. Despite the chaotic nature of these systems,
periodic orbits represent the repetition of certain
states of the system over time. In chaotic systems,
these orbits are usually surrounded by complex,
irregular trajectories, but are themselves defined by
regularity and predictability. We should add that
periodic orbits are important to chaos theory because
they provide a basis for understanding the internal
structure of chaotic systems. Although chaos is defined
by unpredictability based on initial conditions and the
complexity, these periodic orbits represent islands of
predictability that can be analysed and modelled. GP
and its symbolic regression capability is an ideal tool
for finding both stable periodic orbits defined by
stable points and general periodic orbits that rebuild
attractive periodic states for the system. The
objective function is also crucial for finding periodic
orbits using GP. This function has been designed to
achieve stable regions as well as the possibility of
choosing the degree of the orbital. The test problem
will consist of four systems of deterministic chaos,
the so-called chaotic maps - the logistic map, the
Henon map, the Lozi map and the Burgers map.",
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notes = "also known as \cite{10611935}
WCCI 2024",
- }
Genetic Programming entries for
Radomil Matousek
Tomas Hulka
Rene Pierre Lozi
Jakub Kudela
Citations