| Summary: | 博士 === 國立成功大學 === 物理學系 === 87 === In this thesis we study two issues associated with nonlinear oscillators. One concerns about the phenomena of zero-dispersion nonlinear resonance with its abbreviation ZDNR. The other is the research about the phase synchronization between two couple nonlinear oscillators. For the former, we pay a perspective view on its value of application; in the thesis we introduce a method different from that employed in traditional scheme, which greatly simplifies the tedious procedure required as before. With a further study on the influence of noise upon ZDNR, we find an exponential law capable of characteristic description. Subsequently, we present the new phenomena of series of junketed ZDNR. For the latter, we start at the theory of phase synchronization in nonlinear dynamics, and introduce the concept of "amplitude synchronization" to compare with "phase synchronization". We found that phase synchronization is always achieved before that of amplitude synchronization. From this foundation, we interpret that phase synchronization is merely a misleading concept in the process of mathematically nonlinear transformation. Therefore, a reexamination on the thinking of phase synchronization, according to our research, is necessary.
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