Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk System
A multi-scroll attractor reflects the structural diversity of the dynamic system, and multi-stability behavior reflects its state diversity. Multi-scroll and multi-stability chaotic systems can produce complex random sequences, which have important application values in the field of data security. H...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/16/5/2494 |
| _version_ | 1797615356886384640 |
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| author | Fudong Li Jingru Zeng |
| author_facet | Fudong Li Jingru Zeng |
| author_sort | Fudong Li |
| collection | DOAJ |
| description | A multi-scroll attractor reflects the structural diversity of the dynamic system, and multi-stability behavior reflects its state diversity. Multi-scroll and multi-stability chaotic systems can produce complex random sequences, which have important application values in the field of data security. However, current works on multi-scroll–multi-steady behavior have been carried out separately, rather than simultaneously. This paper considers a three-dimensional Jerk system with a sinusoidal nonlinear term. The basic dynamic behaviors, such as the stability of equilibrium points, bifurcation of parameters and initial values, phase diagrams, and basins of attraction, were analyzed. It was found that the system has infinite equilibrium points. Moreover, the system not only generates complex dynamics, such as single-scroll, double-scroll, and multi-scroll but also realizes the self-reproduction of these dynamic characteristics by controlling the initial value of the system. Therefore, by expanding the equilibrium point, the effective controls of the system’s structural diversity and state diversity are realized at the same time, having important theoretical significance and application value. |
| first_indexed | 2024-03-11T07:25:08Z |
| format | Article |
| id | doaj.art-03932f2cded84c6dbc6942ddd0600a98 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-11T07:25:08Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-03932f2cded84c6dbc6942ddd0600a982023-11-17T07:39:23ZengMDPI AGEnergies1996-10732023-03-01165249410.3390/en16052494Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk SystemFudong Li0Jingru Zeng1School of Mechanical and Electrical Engineering, Beijing Information Science and Technology University, Beijing 100192, ChinaDepartment of Electrical Engineering, Chengnan College, Changsha University of Science & Technology, Changsha 410015, ChinaA multi-scroll attractor reflects the structural diversity of the dynamic system, and multi-stability behavior reflects its state diversity. Multi-scroll and multi-stability chaotic systems can produce complex random sequences, which have important application values in the field of data security. However, current works on multi-scroll–multi-steady behavior have been carried out separately, rather than simultaneously. This paper considers a three-dimensional Jerk system with a sinusoidal nonlinear term. The basic dynamic behaviors, such as the stability of equilibrium points, bifurcation of parameters and initial values, phase diagrams, and basins of attraction, were analyzed. It was found that the system has infinite equilibrium points. Moreover, the system not only generates complex dynamics, such as single-scroll, double-scroll, and multi-scroll but also realizes the self-reproduction of these dynamic characteristics by controlling the initial value of the system. Therefore, by expanding the equilibrium point, the effective controls of the system’s structural diversity and state diversity are realized at the same time, having important theoretical significance and application value.https://www.mdpi.com/1996-1073/16/5/2494Jerk systemmulti-scrollmulti-stabilityequilibrium pointdiversity |
| spellingShingle | Fudong Li Jingru Zeng Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk System Energies Jerk system multi-scroll multi-stability equilibrium point diversity |
| title | Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk System |
| title_full | Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk System |
| title_fullStr | Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk System |
| title_full_unstemmed | Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk System |
| title_short | Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk System |
| title_sort | multi scroll attractor and multi stable dynamics of a three dimensional jerk system |
| topic | Jerk system multi-scroll multi-stability equilibrium point diversity |
| url | https://www.mdpi.com/1996-1073/16/5/2494 |
| work_keys_str_mv | AT fudongli multiscrollattractorandmultistabledynamicsofathreedimensionaljerksystem AT jingruzeng multiscrollattractorandmultistabledynamicsofathreedimensionaljerksystem |