A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization
The study of hidden attractors plays a very important role in the engineering applications of nonlinear dynamical systems. In this paper, a new three-dimensional (3D) chaotic system is proposed in which hidden attractors and self-excited attractors appear as the parameters change. Meanwhile, asymmet...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/12/740 |
| _version_ | 1797458281674833920 |
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| author | Jiahui Wang Chengwei Dong Hantao Li |
| author_facet | Jiahui Wang Chengwei Dong Hantao Li |
| author_sort | Jiahui Wang |
| collection | DOAJ |
| description | The study of hidden attractors plays a very important role in the engineering applications of nonlinear dynamical systems. In this paper, a new three-dimensional (3D) chaotic system is proposed in which hidden attractors and self-excited attractors appear as the parameters change. Meanwhile, asymmetric coexisting attractors are also found as a result of the system symmetry. The complex dynamical behaviors of the proposed system were investigated using various tools, including time-series diagrams, Poincaré first return maps, bifurcation diagrams, and basins of attraction. Moreover, the unstable periodic orbits within a topological length of 3 in the hidden chaotic attractor were calculated systematically by the variational method, which required six letters to establish suitable symbolic dynamics. Furthermore, the practicality of the hidden attractor chaotic system was verified by circuit simulations. Finally, offset boosting control and adaptive synchronization were used to investigate the utility of the proposed chaotic system in engineering applications. |
| first_indexed | 2024-03-09T16:34:51Z |
| format | Article |
| id | doaj.art-f93cc1d9e4ba450c88201f89efca4750 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T16:34:51Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-f93cc1d9e4ba450c88201f89efca47502023-11-24T14:57:52ZengMDPI AGFractal and Fractional2504-31102022-12-0161274010.3390/fractalfract6120740A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and SynchronizationJiahui Wang0Chengwei Dong1Hantao Li2Department of Physics, North University of China, Taiyuan 030051, ChinaDepartment of Physics, North University of China, Taiyuan 030051, ChinaDepartment of Physics, North University of China, Taiyuan 030051, ChinaThe study of hidden attractors plays a very important role in the engineering applications of nonlinear dynamical systems. In this paper, a new three-dimensional (3D) chaotic system is proposed in which hidden attractors and self-excited attractors appear as the parameters change. Meanwhile, asymmetric coexisting attractors are also found as a result of the system symmetry. The complex dynamical behaviors of the proposed system were investigated using various tools, including time-series diagrams, Poincaré first return maps, bifurcation diagrams, and basins of attraction. Moreover, the unstable periodic orbits within a topological length of 3 in the hidden chaotic attractor were calculated systematically by the variational method, which required six letters to establish suitable symbolic dynamics. Furthermore, the practicality of the hidden attractor chaotic system was verified by circuit simulations. Finally, offset boosting control and adaptive synchronization were used to investigate the utility of the proposed chaotic system in engineering applications.https://www.mdpi.com/2504-3110/6/12/740hidden attractorunstable periodic orbitcircuit simulationcoexisting attractorsoffset boostingadaptive synchronization |
| spellingShingle | Jiahui Wang Chengwei Dong Hantao Li A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization Fractal and Fractional hidden attractor unstable periodic orbit circuit simulation coexisting attractors offset boosting adaptive synchronization |
| title | A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization |
| title_full | A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization |
| title_fullStr | A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization |
| title_full_unstemmed | A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization |
| title_short | A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization |
| title_sort | new variable boostable 3d chaotic system with hidden and coexisting attractors dynamical analysis periodic orbit coding circuit simulation and synchronization |
| topic | hidden attractor unstable periodic orbit circuit simulation coexisting attractors offset boosting adaptive synchronization |
| url | https://www.mdpi.com/2504-3110/6/12/740 |
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