Dynamic Analysis of a Novel 3D Chaotic System with Hidden and Coexisting Attractors: Offset Boosting, Synchronization, and Circuit Realization
To further understand the dynamical characteristics of chaotic systems with a hidden attractor and coexisting attractors, we investigated the fundamental dynamics of a novel three-dimensional (3D) chaotic system derived by adding a simple constant term to the Yang–Chen system, which includes the bif...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/10/547 |
| _version_ | 1797473214495981568 |
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| author | Chengwei Dong |
| author_facet | Chengwei Dong |
| author_sort | Chengwei Dong |
| collection | DOAJ |
| description | To further understand the dynamical characteristics of chaotic systems with a hidden attractor and coexisting attractors, we investigated the fundamental dynamics of a novel three-dimensional (3D) chaotic system derived by adding a simple constant term to the Yang–Chen system, which includes the bifurcation diagram, Lyapunov exponents spectrum, and basin of attraction, under different parameters. In addition, an offset boosting control method is presented to the state variable, and a numerical simulation of the system is also presented. Furthermore, the unstable cycles embedded in the hidden chaotic attractors are extracted in detail, which shows the effectiveness of the variational method and 1D symbolic dynamics. Finally, the adaptive synchronization of the novel system is successfully designed, and a circuit simulation is implemented to illustrate the flexibility and validity of the numerical results. Theoretical analysis and simulation results indicate that the new system has complex dynamical properties and can be used to facilitate engineering applications. |
| first_indexed | 2024-03-09T20:11:40Z |
| format | Article |
| id | doaj.art-6e85c57b8c4b49679b632ea23751db1b |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T20:11:40Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-6e85c57b8c4b49679b632ea23751db1b2023-11-24T00:11:21ZengMDPI AGFractal and Fractional2504-31102022-09-0161054710.3390/fractalfract6100547Dynamic Analysis of a Novel 3D Chaotic System with Hidden and Coexisting Attractors: Offset Boosting, Synchronization, and Circuit RealizationChengwei Dong0Department of Physics, North University of China, Taiyuan 030051, ChinaTo further understand the dynamical characteristics of chaotic systems with a hidden attractor and coexisting attractors, we investigated the fundamental dynamics of a novel three-dimensional (3D) chaotic system derived by adding a simple constant term to the Yang–Chen system, which includes the bifurcation diagram, Lyapunov exponents spectrum, and basin of attraction, under different parameters. In addition, an offset boosting control method is presented to the state variable, and a numerical simulation of the system is also presented. Furthermore, the unstable cycles embedded in the hidden chaotic attractors are extracted in detail, which shows the effectiveness of the variational method and 1D symbolic dynamics. Finally, the adaptive synchronization of the novel system is successfully designed, and a circuit simulation is implemented to illustrate the flexibility and validity of the numerical results. Theoretical analysis and simulation results indicate that the new system has complex dynamical properties and can be used to facilitate engineering applications.https://www.mdpi.com/2504-3110/6/10/547hidden attractorcoexisting attractorsoffset boostingsymbolic dynamicscircuit simulationadaptive synchronization |
| spellingShingle | Chengwei Dong Dynamic Analysis of a Novel 3D Chaotic System with Hidden and Coexisting Attractors: Offset Boosting, Synchronization, and Circuit Realization Fractal and Fractional hidden attractor coexisting attractors offset boosting symbolic dynamics circuit simulation adaptive synchronization |
| title | Dynamic Analysis of a Novel 3D Chaotic System with Hidden and Coexisting Attractors: Offset Boosting, Synchronization, and Circuit Realization |
| title_full | Dynamic Analysis of a Novel 3D Chaotic System with Hidden and Coexisting Attractors: Offset Boosting, Synchronization, and Circuit Realization |
| title_fullStr | Dynamic Analysis of a Novel 3D Chaotic System with Hidden and Coexisting Attractors: Offset Boosting, Synchronization, and Circuit Realization |
| title_full_unstemmed | Dynamic Analysis of a Novel 3D Chaotic System with Hidden and Coexisting Attractors: Offset Boosting, Synchronization, and Circuit Realization |
| title_short | Dynamic Analysis of a Novel 3D Chaotic System with Hidden and Coexisting Attractors: Offset Boosting, Synchronization, and Circuit Realization |
| title_sort | dynamic analysis of a novel 3d chaotic system with hidden and coexisting attractors offset boosting synchronization and circuit realization |
| topic | hidden attractor coexisting attractors offset boosting symbolic dynamics circuit simulation adaptive synchronization |
| url | https://www.mdpi.com/2504-3110/6/10/547 |
| work_keys_str_mv | AT chengweidong dynamicanalysisofanovel3dchaoticsystemwithhiddenandcoexistingattractorsoffsetboostingsynchronizationandcircuitrealization |