A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design

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Veeman, D, Alanezi, A, Natiq, H, Jafari, S and Abd El-Latif, AA (2022) A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design. Symmetry, 14 (2). ISSN 2073-8994

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Open Access URL: https://doi.org/10.3390/sym14020259 (Published version)

Abstract

Here, a chaotic quadratic oscillator with only squared terms is proposed, which shows various dynamics. The oscillator has eight equilibrium points, and none of them is stable. Various bifurcation diagrams of the oscillator are investigated, and its Lyapunov exponents (LEs) are discussed. The multistability of the oscillator is discussed by plotting bifurcation diagrams with various initiation methods. The basin of attraction of the oscillator is discussed in two planes. Impulsive control is applied to the oscillator to control its chaotic dynamics. Additionally, the circuit is implemented to reveal its feasibility.

Item Type: Article
Uncontrolled Keywords: ATTRACTORS; bifurcation; chaotic circuit; DYNAMICS; HARDWARE IMPLEMENTATION; impulsive control; Multidisciplinary Sciences; multistability; NETWORKS; NONLINEARITY; quadratic oscillator; Science & Technology; Science & Technology - Other Topics; SYNCHRONIZATION; SYSTEM; Science & Technology; Multidisciplinary Sciences; Science & Technology - Other Topics; quadratic oscillator; bifurcation; multistability; impulsive control; chaotic circuit; HARDWARE IMPLEMENTATION; SYSTEM; SYNCHRONIZATION; ATTRACTORS; NONLINEARITY; NETWORKS; DYNAMICS
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Computer Science and Mathematics
Publisher: MDPI
Date of acceptance: 14 December 2021
Date of first compliant Open Access: 3 February 2023
Date Deposited: 03 Feb 2023 10:52
Last Modified: 03 Feb 2023 11:00
DOI or ID number: 10.3390/sym14020259
URI: https://researchonline.ljmu.ac.uk/id/eprint/18801
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