Open AccessTHE EFFECT OF NONLINEAR DAMPING TO A DYNAMICAL SYSTEM WITH CENTER PHASE PORTAIT
Author(s) -
Kus Prihantoso Kurniawan,
Husna Arifah
Publication year - 2016
Publication title -
jurnal sains dasar
Language(s) - English
Resource type - Journals
eISSN - 2443-1273
pISSN - 2085-9872
DOI - 10.21831/jsd.v4i1.8439
Subject(s) - phase portrait , portrait , nonlinear system , bifurcation , center (category theory) , hopf bifurcation , phase (matter) , mathematics , physics , mathematical analysis , quantum mechanics , art history , chemistry , art , crystallography
This paper discusses the effect of nonlinear damping to a 2-dimesional system that has center phase portrait. The phase portraits of the damped system are drawn for 3 different values of parameter. These phase portraits stand as the numerical proof of phase portrait change. To prove the change analiticaly, we use the theorem that guarantee the existence of periodic solution. The result shows that nonlinear damping changes the phase portrait topologically. It means that the system undergoes a generalized Hopf bifurcation. Keywords: generalized Hopf bifurcation, center phase portrait, periodic solution