Limit cycles of generalized Liénard polynomial differential systems via averaging theory
Using the averaging theory of first and second order we study the maximum number of limit cycles of the polynomial differential systems x˙ = y, y˙ = -x - ε(p1(x)y + q1(x)y2) - ε2(p2(x)y + q2(x)y2). which bifurcate from the periodic orbits of the linear center ˙x = y, ˙y = -x. Here ε is a small param...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:150699 |
| Online Access: | https://ddd.uab.cat/record/150699 https://dx.doi.org/urn:doi:10.1016/j.chaos.2014.02.008 |
| Access Level: | Open access |
| Keyword: | Averaging theory Liénard Equations Limit cycles |
| Summary: | Using the averaging theory of first and second order we study the maximum number of limit cycles of the polynomial differential systems x˙ = y, y˙ = -x - ε(p1(x)y + q1(x)y2) - ε2(p2(x)y + q2(x)y2). which bifurcate from the periodic orbits of the linear center ˙x = y, ˙y = -x. Here ε is a small parameter. If the degrees of the polynomials p1, p2, q1 and q2 is n, then we prove that this maximum number is [n/2] using the averaging theory of first order, where [·] denotes the integer part function; and this maximum number is at most n using the averaging theory of second order. |
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