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- Title
EXISTENCE, UNIQUENESS AND OTHER PROPERTIES OF THE LIMIT CYCLE OF A GENERALIZED VAN DER POL EQUATION.
- Authors
IOAKIM, XENAKIS
- Abstract
In this article, we study the bifurcation of limit cycles from the linear oscillator ṡ = y, ẏ = -x in the class ṡ = y, ẏ = -x + εyp+1(1 - x2q), where ε is a small positive parameter tending to 0, p ∈ N0 is even and q ∈ N. We prove that the above differential system, in the global plane where p ∈ N0 is even and q ∈ N, 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 Poincaré's method, and the uniqueness can be derived from the work of Sabatini and Villari [6]. 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 [3] and Moremedi et al. [4].
- Subjects
VAN der Pol equation; ORDINARY differential equations; BIFURCATION theory; LIMIT cycles; HARMONIC oscillators
- Publication
Electronic Journal of Differential Equations, 2014, Vol 2014, p1
- ISSN
1550-6150
- Publication type
Article