In this article, we study the bifurcation of limit cycles from the linear oscillator , in the class
where is a small positive parameter tending to 0, is even and . We prove that the above differential system, in the global plane where is even and , has a unique limit cycle. More specifically, the existence of a limit cycle, which is the main result in this work, is obtained by using the Poincare's method, and the uniqueness can be derived from the work of Sabatini and Villari . We also investigate and some other properties of this unique limit cycle for some special cases of this differential system. Such special cases have been studied by Minorsky  and Moremedi et al .
Submitted June 22, 2013. Published January 10, 2014.
Math Subject Classifications: 34C07, 34C23, 34C25.
Key Words: Generalized Van der Pol equation; limit cycles; existence; uniqueness.
Show me the PDF file (222 KB), TEX file, and other files for this article.
| Xenakis Ioakim |
Department of Mathematics and Statistics
University of Cyprus
P.O. Box 20537, 1678 Nicosia, Cyprus
Return to the EJDE web page