| Summary: | 碩士 === 中原大學 === 電機工程研究所 === 82 === In this thesis, the chaotic phenomena of Van der Pol's
oscillator is analyzed from a qualitative viewpoint. The
circuit shows a great variety of dynamical behavior. It is
modeled by a third-order autonomous ordinary differential
equation. At first, the bifurcations of equilibria are
analyzed. It indicates that pitchfork and Hopf bifurcations can
occur when the parameter is varied. In addition, the
bifurcations of periodic orbits including pitchfork, flip and
Hopf bifurcations are investigated. According to these results,
the detailed bifurcation diagrams are obtained in parameter
space. Furthermore, the simulation results based on the
bifurcation diagrams illustrate that the period-adding, period-
p band, trainsient chaos,intermittency , chaos and chaotic
motion oscillates about k's main frequencies will occur.
Finally, the phenomena of period-doubling, period-adding,
entrainment, burst, chaos, intermittency and trainsient chaos
are observed via the circuit experiments. It is believed that
the analytical and experimental results of this thesis will
help us to understand the complex phenomena of nonlinear
dynamic systems well.
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