Based on the idea of bifurcating a limit cycle from a closed orbit of a nonlinear system, this paper presents a mathematical proof of the pseudooscillator analysis developed recently. The result generalizes the main conclusions of the pseudooscillator analysis, and it can also be used to study the problem of highorder Hopf bifurcation, whose stability requires nonlinear terms with order larger than 3. Two illustrative examples are given for demonstration.
俞亚娟,王在华.伪振子分析法的证明及其在高阶Hopf分岔中的应用[J].动力学与控制学报,2012,10(3):202~208; Yu Yajuan, Wang Zaihua. Proof of the pseudo-oscillator analysis and its application in high-order hopf bifurcation[J]. Journal of Dynamics and Control,2012,10(3):202-208.
