Hartono, Kus Prihantoso Krisnawan, Husna Arifah, Fitriani Yuli Saptaningtyas
The aim of this research is to determine an annulus, which lies on a phase space, as the location of limit cycle of the van der Pol equation. It is assumed that the parameter value of nonlinear term of the van der Pol equation is small enough, that is μ □ 1, such that the investigated problem is categorized as a weakly nonlinear case. The existence of limit cycle of the van der Pol equation has been proven in many references, but the explicit form of the limit cycle equation is very hard to determine analytically. In this research, the limit cycle solution is approached by use of perturbation method. The method is very powerful for such weakly nonlinear case. Based on the result of the approximation, two circles are made inside and outside the limit cycle as its minimum and maximum boundaries. Both circles form an annulus in the shape of ring which is a place for the limit cycle. The annulus has a middle radius 2 units length and the thickness approximately twice of the parameter of the weakly nonlinear term in the van der Pol equation. © 2024 Author(s).
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta, Yogyakarta, Indonesia
