A Study Of Frequency-amplitude Relationship To Relaxation Oscillation

In this thesis we study the frequency-amplitude relationships of relaxation oscilla-tions and non-relaxation oscillations.Firstly, we study autonomous systems. In this part, van der Pol model, Fitzgumo-Nagumo model are shown to exhibit a property that the frequencies of relaxation oscil-lations are tunable to their amplitudes. Next we study INa,p+IK-model and IK+IKir-model. The former is a relaxation oscillation, while the later is not. The results show that under a suitable parameter condition the INa,p+IK-model presents relaxation os-cillation and the frequency is tunable to its amplitude, while the Ik+IKir-model does not present relaxation oscillation and the frequency is not tunable to its amplitude.Secondly, we study non-autonomous systems. In this part we mainly discuss a bistable model in the presence of a periodic driving. The system also presents relaxation oscillation under a suitable parameter condition. The results show that the frequency is(is not) tunable to its amplitude when the relaxation time is sufficiently(not suffi-ciently) large. The comparison in the same model also explains that the frequency of relaxation oscillation is tunable to its amplitude, while the frequency of non-relaxation oscillation is not tunable to its amplitude.For a relaxation oscillation, whether it is autonomous or non-autonomous, it has the property that the frequency is tunable to its amplitude, while for other oscillations they do not have such kind of property.