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Limit cycles near an eye-figure loop in some polynomial Liénard systems.
- Source :
-
Journal of Mathematical Analysis & Applications . Nov2017, Vol. 455 Issue 1, p500-515. 16p. - Publication Year :
- 2017
-
Abstract
- In this paper, we study the number of limit cycles in the family d H − ε ω = 0 , where H = y 2 2 − ∫ 0 x g ( u ) d u , ω = y f ( x ) d x , with g ( x ) = x ( x 2 − 1 ) ( x 2 − 1 4 ) 2 , and f ( x ) an even polynomial of degree 10. We will consider mainly the bifurcation of limit cycles near the eye-figure loop and the center of d H = 0 . Our investigation focuses on the lower bound of the maximal number of limit cycles for these systems. In particular, we show that the perturbed system can have at least 8 limit cycles when deg ( f ( x ) ) = 10 . [ABSTRACT FROM AUTHOR]
- Subjects :
- *LIMIT cycles
*POLYNOMIALS
*NUMBER theory
*BIFURCATION theory
*PERTURBATION theory
Subjects
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 455
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 123759016
- Full Text :
- https://doi.org/10.1016/j.jmaa.2017.05.064