Analysis of torus breakdown into chaos in a constraint Duffing van der Pol oscillator

作者：Sekikawa Munehisa; Inaba Naohiko; Tsubouchi Takashi; Aihara Kazuyuki

来源：International Journal of Bifurcation and Chaos, 2008, 18(4): 1051-1068.

DOI：10.1142/S0218127408020835

• chaos
• torus
• bifurcation
• nonlinear oscillator

The bifurcation structure of a constraint Duffing van der Pol oscillator with a diode is analyzed and an objective bifurcation diagram is illustrated in detail in this work. An idealized case, where the diode is assumed to operate as a switch, is considered.
In this case, the Poincare map is constructed as a one-dimensional map: a circle map. The parameter boundary between a torus-generating region where the circle map is a diffeomorphism and a chaos-generating region where the circle map has extrema is derived explicitly, without solving the implicit equations, by adopting some novel ideas. On the bifurcation diagram, intermittency and a saddle-node bifurcation from the periodic state to the quasi-periodic state can be exactly distinguished. Laboratory experiment is also carried out and theoretical results are verified.

• 出版日期2008-4
• 单位中国地震局工程力学研究所