Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems
The main purpose of this paper is to investigate the mechanism of sliding phenomenon in Filippov (nonsmooth) dynamical systems by attractor analysis and vector analysis. A corresponding simple model based on Chua’s circuit with periodic excitation was introduced as an example. The attractor analysis...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2019/8213808 |
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| _version_ | 1832556515859365888 |
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| author | Rui Qu Shaolong Li |
| author_facet | Rui Qu Shaolong Li |
| author_sort | Rui Qu |
| collection | DOAJ |
| description | The main purpose of this paper is to investigate the mechanism of sliding phenomenon in Filippov (nonsmooth) dynamical systems by attractor analysis and vector analysis. A corresponding simple model based on Chua’s circuit with periodic excitation was introduced as an example. The attractor analysis proposed in our previous work is used to discuss the complicated oscillations of the Filippov system. However, it failed to perfectly explain the sliding phenomena and establish an analytical method of constant voltage control. Therefore, the geometric structure and analytic conditions of sliding bifurcations in the general n-dimensional piecewise smooth system are discussed in detail by vector structure analysis. The prospects of practical application of this method are also discussed in the end. |
| format | Article |
| id | doaj-art-1d813c232e924b1eaf632e42214f1e9e |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-1d813c232e924b1eaf632e42214f1e9e2025-02-03T05:45:12ZengWileyShock and Vibration1070-96221875-92032019-01-01201910.1155/2019/82138088213808Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov SystemsRui Qu0Shaolong Li1Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, ChinaFaculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, ChinaThe main purpose of this paper is to investigate the mechanism of sliding phenomenon in Filippov (nonsmooth) dynamical systems by attractor analysis and vector analysis. A corresponding simple model based on Chua’s circuit with periodic excitation was introduced as an example. The attractor analysis proposed in our previous work is used to discuss the complicated oscillations of the Filippov system. However, it failed to perfectly explain the sliding phenomena and establish an analytical method of constant voltage control. Therefore, the geometric structure and analytic conditions of sliding bifurcations in the general n-dimensional piecewise smooth system are discussed in detail by vector structure analysis. The prospects of practical application of this method are also discussed in the end.http://dx.doi.org/10.1155/2019/8213808 |
| spellingShingle | Rui Qu Shaolong Li Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems Shock and Vibration |
| title | Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems |
| title_full | Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems |
| title_fullStr | Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems |
| title_full_unstemmed | Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems |
| title_short | Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems |
| title_sort | attractor and vector structure analyses of bursting oscillation with sliding bifurcation in filippov systems |
| url | http://dx.doi.org/10.1155/2019/8213808 |
| work_keys_str_mv | AT ruiqu attractorandvectorstructureanalysesofburstingoscillationwithslidingbifurcationinfilippovsystems AT shaolongli attractorandvectorstructureanalysesofburstingoscillationwithslidingbifurcationinfilippovsystems |