Dynamic Analysis of a One-Parameter Chaotic System in Complex Field
Chaotic dynamics analysis of complex-variable chaotic systems (CVCSs) is an important problem in real secure communication and encryption. In this paper, a simple one-parameter chaotic system in complex field is proposed, whose nonlinear terms are the same as Lorenz system but the linear terms are m...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8963938/ |
| _version_ | 1828977417191948288 |
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| author | Xiu Zhao Jian Liu Hongjun Liu Fangfang Zhang |
| author_facet | Xiu Zhao Jian Liu Hongjun Liu Fangfang Zhang |
| author_sort | Xiu Zhao |
| collection | DOAJ |
| description | Chaotic dynamics analysis of complex-variable chaotic systems (CVCSs) is an important problem in real secure communication and encryption. In this paper, a simple one-parameter chaotic system in complex field is proposed, whose nonlinear terms are the same as Lorenz system but the linear terms are much simpler. The proposed system has circular equilibria and therefore multi-stability can be measured by phase portraits, bifurcation diagrams and Lyapunov exponent spectrum. Its basin of attraction is filled with initial points leading to chaotic behaviors. The coexistence of infinitely many attractors is found in the proposed system, which is not reported in the existing complex-variable Lorenz system. Finally, two complexity indexes are used to measure dynamic characteristic with respect to parameter. |
| first_indexed | 2024-12-14T14:57:12Z |
| format | Article |
| id | doaj.art-0f990693e06d499e867c802c11d7a0f8 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-14T14:57:12Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-0f990693e06d499e867c802c11d7a0f82022-12-21T22:56:57ZengIEEEIEEE Access2169-35362020-01-018287742878110.1109/ACCESS.2020.29682268963938Dynamic Analysis of a One-Parameter Chaotic System in Complex FieldXiu Zhao0https://orcid.org/0000-0002-5478-5363Jian Liu1https://orcid.org/0000-0001-9386-5406Hongjun Liu2https://orcid.org/0000-0003-4991-6696Fangfang Zhang3https://orcid.org/0000-0002-9254-3525School of Mathematical Sciences, University of Jinan, Jinan, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, ChinaDepartment of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan, ChinaChaotic dynamics analysis of complex-variable chaotic systems (CVCSs) is an important problem in real secure communication and encryption. In this paper, a simple one-parameter chaotic system in complex field is proposed, whose nonlinear terms are the same as Lorenz system but the linear terms are much simpler. The proposed system has circular equilibria and therefore multi-stability can be measured by phase portraits, bifurcation diagrams and Lyapunov exponent spectrum. Its basin of attraction is filled with initial points leading to chaotic behaviors. The coexistence of infinitely many attractors is found in the proposed system, which is not reported in the existing complex-variable Lorenz system. Finally, two complexity indexes are used to measure dynamic characteristic with respect to parameter.https://ieeexplore.ieee.org/document/8963938/Coexisting attractorsextreme multistabilitycomplex-variable chaotic systemcomplexity |
| spellingShingle | Xiu Zhao Jian Liu Hongjun Liu Fangfang Zhang Dynamic Analysis of a One-Parameter Chaotic System in Complex Field IEEE Access Coexisting attractors extreme multistability complex-variable chaotic system complexity |
| title | Dynamic Analysis of a One-Parameter Chaotic System in Complex Field |
| title_full | Dynamic Analysis of a One-Parameter Chaotic System in Complex Field |
| title_fullStr | Dynamic Analysis of a One-Parameter Chaotic System in Complex Field |
| title_full_unstemmed | Dynamic Analysis of a One-Parameter Chaotic System in Complex Field |
| title_short | Dynamic Analysis of a One-Parameter Chaotic System in Complex Field |
| title_sort | dynamic analysis of a one parameter chaotic system in complex field |
| topic | Coexisting attractors extreme multistability complex-variable chaotic system complexity |
| url | https://ieeexplore.ieee.org/document/8963938/ |
| work_keys_str_mv | AT xiuzhao dynamicanalysisofaoneparameterchaoticsystemincomplexfield AT jianliu dynamicanalysisofaoneparameterchaoticsystemincomplexfield AT hongjunliu dynamicanalysisofaoneparameterchaoticsystemincomplexfield AT fangfangzhang dynamicanalysisofaoneparameterchaoticsystemincomplexfield |