On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems
We study the number of limit cycles for the quadratic polynomial differential systems x˙=-y+x2, y˙=x+xy having an isochronous center with continuous and discontinuous cubic polynomial perturbations. Using the averaging theory of first order, we obtain that 3 limit cycles bifurcate from the periodic...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/4939780 |
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| _version_ | 1832552621981827072 |
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| author | Ziguo Jiang |
| author_facet | Ziguo Jiang |
| author_sort | Ziguo Jiang |
| collection | DOAJ |
| description | We study the number of limit cycles for the quadratic polynomial differential systems x˙=-y+x2, y˙=x+xy having an isochronous center with continuous and discontinuous cubic polynomial perturbations. Using the averaging theory of first order, we obtain that 3 limit cycles bifurcate from the periodic orbits of the isochronous center with continuous perturbations and at least 7 limit cycles bifurcate from the periodic orbits of the isochronous center with discontinuous perturbations. Moreover, this work shows that the discontinuous systems have at least 4 more limit cycles surrounding the origin than the continuous ones. |
| format | Article |
| id | doaj-art-1ec0deb42a78416cb485931b12a8c757 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-1ec0deb42a78416cb485931b12a8c7572025-02-03T05:58:09ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/49397804939780On the Limit Cycles for Continuous and Discontinuous Cubic Differential SystemsZiguo Jiang0Department of Mathematics and Finances, Aba Teachers University, Wenchuan, Sichuan 623002, ChinaWe study the number of limit cycles for the quadratic polynomial differential systems x˙=-y+x2, y˙=x+xy having an isochronous center with continuous and discontinuous cubic polynomial perturbations. Using the averaging theory of first order, we obtain that 3 limit cycles bifurcate from the periodic orbits of the isochronous center with continuous perturbations and at least 7 limit cycles bifurcate from the periodic orbits of the isochronous center with discontinuous perturbations. Moreover, this work shows that the discontinuous systems have at least 4 more limit cycles surrounding the origin than the continuous ones.http://dx.doi.org/10.1155/2016/4939780 |
| spellingShingle | Ziguo Jiang On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems Discrete Dynamics in Nature and Society |
| title | On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems |
| title_full | On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems |
| title_fullStr | On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems |
| title_full_unstemmed | On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems |
| title_short | On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems |
| title_sort | on the limit cycles for continuous and discontinuous cubic differential systems |
| url | http://dx.doi.org/10.1155/2016/4939780 |
| work_keys_str_mv | AT ziguojiang onthelimitcyclesforcontinuousanddiscontinuouscubicdifferentialsystems |