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Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System

In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalize...

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Autores principales: Wang, Ze, Qi, Guoyuan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7823887/
https://www.ncbi.nlm.nih.gov/pubmed/33406791
http://dx.doi.org/10.3390/e23010071
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author Wang, Ze
Qi, Guoyuan
author_facet Wang, Ze
Qi, Guoyuan
author_sort Wang, Ze
collection PubMed
description In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalized Hamiltonian energy function has been given, and it is composed of conservative and non-conservative parts of the Hamiltonian. The Hamiltonian of the Euler equation remains constant, while the three-terminal memristor’s Hamiltonian is mutative, causing non-conservation in energy. Through proof, only centers or saddles equilibria exist, which meets the definition of the conservative system. A non-Hamiltonian conservative chaotic system is proposed. The Hamiltonian of the conservative part determines whether the system can produce chaos or not. The non-conservative part affects the dynamic of the system based on the conservative part. The chaotic and quasiperiodic orbits are generated when the system has different Hamiltonian levels. Lyapunov exponent (LE), Poincaré map, bifurcation and Hamiltonian diagrams are used to analyze the dynamical behavior of the non-Hamiltonian conservative chaotic system. The frequency and initial values of the system have an extensive variable range. Through the mechanism adjustment, instead of trial-and-error, the maximum LE of the system can even reach an incredible value of 963. An analog circuit is implemented to verify the existence of the non-Hamiltonian conservative chaotic system, which overcomes the challenge that a little bias will lead to the disappearance of conservative chaos.
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spelling pubmed-78238872021-02-24 Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System Wang, Ze Qi, Guoyuan Entropy (Basel) Article In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalized Hamiltonian energy function has been given, and it is composed of conservative and non-conservative parts of the Hamiltonian. The Hamiltonian of the Euler equation remains constant, while the three-terminal memristor’s Hamiltonian is mutative, causing non-conservation in energy. Through proof, only centers or saddles equilibria exist, which meets the definition of the conservative system. A non-Hamiltonian conservative chaotic system is proposed. The Hamiltonian of the conservative part determines whether the system can produce chaos or not. The non-conservative part affects the dynamic of the system based on the conservative part. The chaotic and quasiperiodic orbits are generated when the system has different Hamiltonian levels. Lyapunov exponent (LE), Poincaré map, bifurcation and Hamiltonian diagrams are used to analyze the dynamical behavior of the non-Hamiltonian conservative chaotic system. The frequency and initial values of the system have an extensive variable range. Through the mechanism adjustment, instead of trial-and-error, the maximum LE of the system can even reach an incredible value of 963. An analog circuit is implemented to verify the existence of the non-Hamiltonian conservative chaotic system, which overcomes the challenge that a little bias will lead to the disappearance of conservative chaos. MDPI 2021-01-04 /pmc/articles/PMC7823887/ /pubmed/33406791 http://dx.doi.org/10.3390/e23010071 Text en © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Wang, Ze
Qi, Guoyuan
Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System
title Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System
title_full Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System
title_fullStr Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System
title_full_unstemmed Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System
title_short Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System
title_sort modeling and analysis of a three-terminal-memristor-based conservative chaotic system
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7823887/
https://www.ncbi.nlm.nih.gov/pubmed/33406791
http://dx.doi.org/10.3390/e23010071
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