Stability Analysis of Limit Cycle on Single Nonlinear Oscillator Model
Nahrul Mubarok, Rudy Kusdiantara, Nuning Nuraini

Institut Teknologi Bandung

Abstract

An oscillator is a tool that is widely applied in everyday life because of its ability to produce oscillatory motion without the need for continuous external force. To get the desired motion, it is necessary to analyze the bifurcation of the external force parameters of the oscillator system. The oscillatory motion result can be viewed as a periodic solution based on the system of differential equations which is modelled by an oscillator system. In this paper, we propose a scaling method that can be used to find the periodic solution (limit cycle) of an oscillator equation. This method will be used to find a periodic solution of the oscillator model with a nonlinear force and its period. The stability of the periodic solution can be determined by using the Floquet theory. We also perform pseudo-arclength continuation to obtain the bifurcation diagram when linear damping, i.e., the bifurcation parameter varies. This method is quite effective in obtaining the bifurcation diagram when the solution branches have a turning point. By using this method, the behaviour of the oscillator system can be categorized into three cases with respect to changes in the linear damping parameter.

Keywords: nonlinear oscillator, limit cycle, Floquet theory, numerical continuation, bifurcation diagram

Topic: MATHEMATICS AND STATISTICS