Dynamics, Periodic Orbit Analysis, and Circuit Implementation of a New Chaotic System with Hidden Attractor
Hidden attractors are associated with multistability phenomena, which have considerable application prospects in engineering. By modifying a simple three-dimensional continuous quadratic dynamical system, this paper reports a new autonomous chaotic system with two stable node-foci that can generate...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/4/190 |
| _version_ | 1797504800248561664 |
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| author | Chengwei Dong |
| author_facet | Chengwei Dong |
| author_sort | Chengwei Dong |
| collection | DOAJ |
| description | Hidden attractors are associated with multistability phenomena, which have considerable application prospects in engineering. By modifying a simple three-dimensional continuous quadratic dynamical system, this paper reports a new autonomous chaotic system with two stable node-foci that can generate double-wing hidden chaotic attractors. We discuss the rich dynamics of the proposed system, which have some interesting characteristics for different parameters and initial conditions, through the use of dynamic analysis tools such as the phase portrait, Lyapunov exponent spectrum, and bifurcation diagram. The topological classification of the periodic orbits of the system is investigated by a recently devised variational method. Symbolic dynamics of four and six letters are successfully established under two sets of system parameters, including hidden and self-excited chaotic attractors. The system is implemented by a corresponding analog electronic circuit to verify its realizability. |
| first_indexed | 2024-03-10T04:09:31Z |
| format | Article |
| id | doaj.art-b5e3dec491bb4854a2229ff4faabd6c4 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:09:31Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-b5e3dec491bb4854a2229ff4faabd6c42023-11-23T08:15:18ZengMDPI AGFractal and Fractional2504-31102022-03-016419010.3390/fractalfract6040190Dynamics, Periodic Orbit Analysis, and Circuit Implementation of a New Chaotic System with Hidden AttractorChengwei Dong0Department of Physics, North University of China, Taiyuan 030051, ChinaHidden attractors are associated with multistability phenomena, which have considerable application prospects in engineering. By modifying a simple three-dimensional continuous quadratic dynamical system, this paper reports a new autonomous chaotic system with two stable node-foci that can generate double-wing hidden chaotic attractors. We discuss the rich dynamics of the proposed system, which have some interesting characteristics for different parameters and initial conditions, through the use of dynamic analysis tools such as the phase portrait, Lyapunov exponent spectrum, and bifurcation diagram. The topological classification of the periodic orbits of the system is investigated by a recently devised variational method. Symbolic dynamics of four and six letters are successfully established under two sets of system parameters, including hidden and self-excited chaotic attractors. The system is implemented by a corresponding analog electronic circuit to verify its realizability.https://www.mdpi.com/2504-3110/6/4/190hidden attractorunstable periodic orbitsymbolic dynamicselectronic circuit |
| spellingShingle | Chengwei Dong Dynamics, Periodic Orbit Analysis, and Circuit Implementation of a New Chaotic System with Hidden Attractor Fractal and Fractional hidden attractor unstable periodic orbit symbolic dynamics electronic circuit |
| title | Dynamics, Periodic Orbit Analysis, and Circuit Implementation of a New Chaotic System with Hidden Attractor |
| title_full | Dynamics, Periodic Orbit Analysis, and Circuit Implementation of a New Chaotic System with Hidden Attractor |
| title_fullStr | Dynamics, Periodic Orbit Analysis, and Circuit Implementation of a New Chaotic System with Hidden Attractor |
| title_full_unstemmed | Dynamics, Periodic Orbit Analysis, and Circuit Implementation of a New Chaotic System with Hidden Attractor |
| title_short | Dynamics, Periodic Orbit Analysis, and Circuit Implementation of a New Chaotic System with Hidden Attractor |
| title_sort | dynamics periodic orbit analysis and circuit implementation of a new chaotic system with hidden attractor |
| topic | hidden attractor unstable periodic orbit symbolic dynamics electronic circuit |
| url | https://www.mdpi.com/2504-3110/6/4/190 |
| work_keys_str_mv | AT chengweidong dynamicsperiodicorbitanalysisandcircuitimplementationofanewchaoticsystemwithhiddenattractor |