Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system
© 2017 Elsevier LtdThis paper demonstrates the existence of Feigenbaum's constants in reverse bifurcation for fractional-order Rössler system. First, the numerical algorithm of fractional-order Rössler system is presented. Then, the definition of Feigenbaum's constants in reverse bifurcati...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
American Institute of Physics
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/52372 |
| _version_ | 1848758911718391808 |
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| author | Li, Z. Chen, D. Ma, M. Zhang, Xinguang Wu, Yong Hong |
| author_facet | Li, Z. Chen, D. Ma, M. Zhang, Xinguang Wu, Yong Hong |
| author_sort | Li, Z. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2017 Elsevier LtdThis paper demonstrates the existence of Feigenbaum's constants in reverse bifurcation for fractional-order Rössler system. First, the numerical algorithm of fractional-order Rössler system is presented. Then, the definition of Feigenbaum's constants in reverse bifurcation is provided. Third, in order to observe the effect of fractional-order to Feigenbaum's constants in reverse bifurcation, a series of bifurcation diagrams are computed. The Feigenbaum's constants in reverse bifurcation are measured and the error percentage in fractional-order Rössler system is presented. The simulation results show that Feigenbaum's constants exist in reverse bifurcation for fractional-order Rössler system. Especially, the Feigenbaum's constants still exist in the periodic windows. A summary on previous others’ works about Feigenbaum's constants is proposed. This paper draw a conclusion that the constants are universal in both period-doubling bifurcation and reverse bifurcation for both integer and fractional-order system. |
| first_indexed | 2025-11-14T09:51:31Z |
| format | Journal Article |
| id | curtin-20.500.11937-52372 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:51:31Z |
| publishDate | 2017 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-523722017-09-13T15:40:03Z Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system Li, Z. Chen, D. Ma, M. Zhang, Xinguang Wu, Yong Hong © 2017 Elsevier LtdThis paper demonstrates the existence of Feigenbaum's constants in reverse bifurcation for fractional-order Rössler system. First, the numerical algorithm of fractional-order Rössler system is presented. Then, the definition of Feigenbaum's constants in reverse bifurcation is provided. Third, in order to observe the effect of fractional-order to Feigenbaum's constants in reverse bifurcation, a series of bifurcation diagrams are computed. The Feigenbaum's constants in reverse bifurcation are measured and the error percentage in fractional-order Rössler system is presented. The simulation results show that Feigenbaum's constants exist in reverse bifurcation for fractional-order Rössler system. Especially, the Feigenbaum's constants still exist in the periodic windows. A summary on previous others’ works about Feigenbaum's constants is proposed. This paper draw a conclusion that the constants are universal in both period-doubling bifurcation and reverse bifurcation for both integer and fractional-order system. 2017 Journal Article http://hdl.handle.net/20.500.11937/52372 10.1016/j.chaos.2017.03.014 American Institute of Physics restricted |
| spellingShingle | Li, Z. Chen, D. Ma, M. Zhang, Xinguang Wu, Yong Hong Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system |
| title | Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system |
| title_full | Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system |
| title_fullStr | Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system |
| title_full_unstemmed | Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system |
| title_short | Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system |
| title_sort | feigenbaum's constants in reverse bifurcation of fractional-order rössler system |
| url | http://hdl.handle.net/20.500.11937/52372 |