Nonlinear Dynamical Bifurcation Analysis of Van der Pol-Duffing Equation
Xu Lei(1), Lu Mingwan(1), Can Qingjie(2)
(1 Department of Engineering Mechanics, Tsinghua University, Beijing, China, 100084) 
(2 School of Mathematics and System Science, Shandong University, Jinan, China, 250061)

Abstract: By the averaging method, the frequency-amplitude property of Van der Pol-Duffing equation is analyzed, and the related static bifurcation phenomenon is studied by the theory of singularity. Further research on dynamical bifureation finds out that the system displays different phase space properties as the sys tem parameters vary from one region to another. Meanwhile, coexistence of multiple attractors is analyzed with cell-to-cell mapping method.
Keywords: Averaged system bifurcation, attractor, Cell-to-Cell mapping.