Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System
In this paper, an incommensurate fractional-order chaotic system is established based on Chua’s system. Combining fractional-order calculus theory and the Adomian algorithm, the dynamic phenomena of the incommensurate system caused by different fractional orders are studied. Meanwhile, the incommens...
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MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/18 |
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| author | Xianchen Wang Zhen Wang Shihong Dang |
| author_facet | Xianchen Wang Zhen Wang Shihong Dang |
| author_sort | Xianchen Wang |
| collection | DOAJ |
| description | In this paper, an incommensurate fractional-order chaotic system is established based on Chua’s system. Combining fractional-order calculus theory and the Adomian algorithm, the dynamic phenomena of the incommensurate system caused by different fractional orders are studied. Meanwhile, the incommensurate system parameters and initial values are used as variables to study the dynamic characteristics of the incommensurate system. It is found that there are rich coexistence bifurcation diagrams and coexistence Lyapunov exponent spectra which are further verified with the phase diagrams. Moreover, a special dynamic phenomenon, such as chaotic degenerate dynamic behavior, is found in the incommensurate system. Secondly, for the feasibility of practical application, the equivalent analog circuit of incommensurate system is realized according to fractional-order time–frequency frequency domain algorithm. Finally, in order to overcome the limitation that the convergence time of the finite-time synchronization control scheme depends on the initial value, a fixed-time synchronization control scheme is proposed in the selection of synchronization control scheme. The rationality of this scheme is proved by theoretical analysis and numerical simulation. |
| format | Article |
| id | doaj-art-f40ae2926a5042eebba159ae2b812842 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-f40ae2926a5042eebba159ae2b8128422025-01-24T13:33:23ZengMDPI AGFractal and Fractional2504-31102024-12-01911810.3390/fractalfract9010018Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic SystemXianchen Wang0Zhen Wang1Shihong Dang2School of Electronics and Communication Engineering, Shenzhen Polytechnic University, Shenzhen 518055, ChinaSchool of Mathematics and Computer Science, Yan’an University, Yan’an 716000, ChinaInstitute of Electromechanical (Technician), Xianyang Vocational and Technical College, Xianyang 712000, ChinaIn this paper, an incommensurate fractional-order chaotic system is established based on Chua’s system. Combining fractional-order calculus theory and the Adomian algorithm, the dynamic phenomena of the incommensurate system caused by different fractional orders are studied. Meanwhile, the incommensurate system parameters and initial values are used as variables to study the dynamic characteristics of the incommensurate system. It is found that there are rich coexistence bifurcation diagrams and coexistence Lyapunov exponent spectra which are further verified with the phase diagrams. Moreover, a special dynamic phenomenon, such as chaotic degenerate dynamic behavior, is found in the incommensurate system. Secondly, for the feasibility of practical application, the equivalent analog circuit of incommensurate system is realized according to fractional-order time–frequency frequency domain algorithm. Finally, in order to overcome the limitation that the convergence time of the finite-time synchronization control scheme depends on the initial value, a fixed-time synchronization control scheme is proposed in the selection of synchronization control scheme. The rationality of this scheme is proved by theoretical analysis and numerical simulation.https://www.mdpi.com/2504-3110/9/1/18incommensurate fractional orderAdomian algorithmanalog circuitfixed-time synchronization control |
| spellingShingle | Xianchen Wang Zhen Wang Shihong Dang Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System Fractal and Fractional incommensurate fractional order Adomian algorithm analog circuit fixed-time synchronization control |
| title | Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System |
| title_full | Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System |
| title_fullStr | Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System |
| title_full_unstemmed | Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System |
| title_short | Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System |
| title_sort | dynamic behavior and fixed time synchronization control of incommensurate fractional order chaotic system |
| topic | incommensurate fractional order Adomian algorithm analog circuit fixed-time synchronization control |
| url | https://www.mdpi.com/2504-3110/9/1/18 |
| work_keys_str_mv | AT xianchenwang dynamicbehaviorandfixedtimesynchronizationcontrolofincommensuratefractionalorderchaoticsystem AT zhenwang dynamicbehaviorandfixedtimesynchronizationcontrolofincommensuratefractionalorderchaoticsystem AT shihongdang dynamicbehaviorandfixedtimesynchronizationcontrolofincommensuratefractionalorderchaoticsystem |