Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations
In this paper, bifurcation points of two chaotic maps are studied: symmetric sine map and Gaussian map. Investigating the properties of these maps shows that they have a variety of dynamical solutions by changing the bifurcation parameter. Sine map has symmetry with respect to the origin, which caus...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/9927607 |
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| author | Changzhi Li Dhanagopal Ramachandran Karthikeyan Rajagopal Sajad Jafari Yongjian Liu |
| author_facet | Changzhi Li Dhanagopal Ramachandran Karthikeyan Rajagopal Sajad Jafari Yongjian Liu |
| author_sort | Changzhi Li |
| collection | DOAJ |
| description | In this paper, bifurcation points of two chaotic maps are studied: symmetric sine map and Gaussian map. Investigating the properties of these maps shows that they have a variety of dynamical solutions by changing the bifurcation parameter. Sine map has symmetry with respect to the origin, which causes multistability in its dynamics. The systems’ bifurcation diagrams show various dynamics and bifurcation points. Predicting bifurcation points of dynamical systems is vital. Any bifurcation can cause a huge wanted/unwanted change in the states of a system. Thus, their predictions are essential in order to be prepared for the changes. Here, the systems’ bifurcations are studied using three indicators of critical slowing down: modified autocorrelation method, modified variance method, and Lyapunov exponent. The results present the efficiency of these indicators in predicting bifurcation points. |
| format | Article |
| id | doaj-art-0a258fbc10c4478cb7f7a724e6eac028 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-0a258fbc10c4478cb7f7a724e6eac0282025-08-20T03:55:27ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/99276079927607Predicting Tipping Points in Chaotic Maps with Period-Doubling BifurcationsChangzhi Li0Dhanagopal Ramachandran1Karthikeyan Rajagopal2Sajad Jafari3Yongjian Liu4Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, ChinaCenter for System Design, Chennai Institute of Technology, Chennai, IndiaCenter for Nonlinear Systems, Chennai Institute of Technology, Chennai, IndiaCenter for Computational Biology, Chennai Institute of Technology, Chennai, IndiaGuangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, ChinaIn this paper, bifurcation points of two chaotic maps are studied: symmetric sine map and Gaussian map. Investigating the properties of these maps shows that they have a variety of dynamical solutions by changing the bifurcation parameter. Sine map has symmetry with respect to the origin, which causes multistability in its dynamics. The systems’ bifurcation diagrams show various dynamics and bifurcation points. Predicting bifurcation points of dynamical systems is vital. Any bifurcation can cause a huge wanted/unwanted change in the states of a system. Thus, their predictions are essential in order to be prepared for the changes. Here, the systems’ bifurcations are studied using three indicators of critical slowing down: modified autocorrelation method, modified variance method, and Lyapunov exponent. The results present the efficiency of these indicators in predicting bifurcation points.http://dx.doi.org/10.1155/2021/9927607 |
| spellingShingle | Changzhi Li Dhanagopal Ramachandran Karthikeyan Rajagopal Sajad Jafari Yongjian Liu Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations Complexity |
| title | Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations |
| title_full | Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations |
| title_fullStr | Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations |
| title_full_unstemmed | Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations |
| title_short | Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations |
| title_sort | predicting tipping points in chaotic maps with period doubling bifurcations |
| url | http://dx.doi.org/10.1155/2021/9927607 |
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