Forced Van Der Pol's Equation

Author
Wallace, Homer
View Count
2608
License
Creative Commons CC BY 4.0
Abstract

This work is going to analyze the Forced Van Der Pol's Equation which is used to analyze the electric circuit. In 1927, Balthasar Van Der Pol observed the stable oscillation and heard some irregular noise in vacuum tube circuit. He then proposed the Forced Van Der Pol's Equation to analyze the circuit and suggested the concept of limit cycle and Chaos to explain his observation. In this work, We would like to analyze behavior of the model by observing the phase space, time series, bifurcation diagram and power spectrum. Those points in the figures are calculated by Runge-Kutta Method with the aid of MATLAB. For a better understanding, the RLC circuit, which is a electric circuit consisting the a resistor, an inductor and a capacitor, will be used as an example for explaining the properties. Apart from electric circuit, the Forced Van Der Pol's Equation can be applied to dynamic systems in different aspect, such as the artificial heart, economic market and so on. Therefore, we suggest this work to all students since the Forced Van Der Pol's Equation can be applied to many majors, like Mathematics, Physics, Economics, Sociology, Biology, Engineering and so on.

Forced Van Der Pol's Equation