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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |