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2016•Jurnal Sains DasarOpen access

THE EFFECT OF NONLINEAR DAMPING TO A DYNAMICAL SYSTEM WITH CENTER PHASE PORTAIT

Kus Prihantoso Kurniawan, Husna Arifah

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Abstract

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

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What this paper is about

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

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Available abstract

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

Key concepts: Phase portrait, Portrait, Nonlinear system, Bifurcation, Center (category theory), Hopf bifurcation, Phase (matter), Mathematics

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