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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/1/71 |
| _version_ | 1797542390167240704 |
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| author | Ze Wang Guoyuan Qi |
| author_facet | Ze Wang Guoyuan Qi |
| author_sort | Ze Wang |
| collection | DOAJ |
| 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 (<i>LE</i>), 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 <i>LE</i> 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. |
| first_indexed | 2024-03-10T13:29:55Z |
| format | Article |
| id | doaj.art-55ed4fe92c414b30a4272bf30663f449 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T13:29:55Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-55ed4fe92c414b30a4272bf30663f4492023-11-21T08:11:48ZengMDPI AGEntropy1099-43002021-01-012317110.3390/e23010071Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic SystemZe Wang0Guoyuan Qi1Tianjin Key Laboratory of Advanced Technology of Electrical Engineering and Energy, Tiangong University, Tianjin 300387, ChinaTianjin Key Laboratory of Advanced Technology of Electrical Engineering and Energy, Tiangong University, Tianjin 300387, ChinaIn 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 (<i>LE</i>), 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 <i>LE</i> 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.https://www.mdpi.com/1099-4300/23/1/71three-terminal memristornon-Hamiltonian conservative chaotic systemconservative chaosanalog circuit |
| spellingShingle | Ze Wang Guoyuan Qi Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System Entropy three-terminal memristor non-Hamiltonian conservative chaotic system conservative chaos analog circuit |
| 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 | three-terminal memristor non-Hamiltonian conservative chaotic system conservative chaos analog circuit |
| url | https://www.mdpi.com/1099-4300/23/1/71 |
| work_keys_str_mv | AT zewang modelingandanalysisofathreeterminalmemristorbasedconservativechaoticsystem AT guoyuanqi modelingandanalysisofathreeterminalmemristorbasedconservativechaoticsystem |