Semi-Stable Periodic Orbits of the Deterministic Chaotic Systems Designed by means of Genetic Programming

článek ve sborníku ve WoS nebo Scopus

angličtina

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 analyzed and modeled. 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.

Chaos control; Genetic programming; Periodic orbit; Optimization; Semi-stable

MATOUŠEK, R.; HŮLKA, T.; LOZI, R.; KŮDELA, J.

8. 8. 2024

IEEE

979-8-3503-0836-5

2024 IEEE Congress on Evolutionary Computation (CEC)

IEEE Xplore

7

https://ieeexplore.ieee.org/document/10611935