Analytical solutions for period-m motions in a periodically forced van der Pol oscillator

Abstract

Approximate, analytical solutions of period-m motions in a periodically forced, van der Pol oscillator are obtained through the Fourier series expression, and the corresponding stability and bifurcation analysis of such period-m motions are carried out. To verify the approximate, analytical solutions of period-m motions, numerical simulations are performed, and the numerical results are compared with analytical solutions. The harmonic amplitude distributions are presented to show the significance of harmonic terms in the finite Fourier series expression of the analytical periodic solutions. Period-m motions are separated by quasi-periodic motion or chaos, and the stable period-m motions are in independent periodic motion windows.