Kinetic Analysis And Its Applications, Two Types Of Oscillations In The Discrete And Continuous Dynamics Model

Oscillating behaviors generated by two types of two-dimensional discrete and continuous models are investigated in the paper. Firstly, the dynamics of an ideal energy-storage-and-releasing model described by a two-dimensional discrete dynami-cal system is analyzed. In light of the Neimark-Sacker bifurcation theory, theoretical results that demonstrate the existence of oscillating behaviors are presented. Then, the model is extended to a more general situation where chaotic dynamics emerge. In the second part of this thesis, the problem of the Frequency Modulation (FM) and the Amplitude Modulation (AM) of an oscillator described by a two-dimensional continuous dynamical system is discussed. The problem is first investigated for the normal form characterized by the Andronov-Hopf bifurcation, and then for a repre-sentative model, the FitzHuge-Nagumo Model. In particular, some typical methods and techniques, such as the Friedrich-Lyapunov theory and the center-manifold the-ory, are used in the investigation.