The homotopy analysis is performed for the Duffing-harmonic oscillator.

Squeezing of even and odd generalized coherent states of non-harmonic oscillator in a finite-dimensional Hilbert space;

Discussion on rotating trap of two-dimensional harmonic oscillator

The principle of operation and design of the harmonic oscillator was introduced and the factors influencing the etching quality of the harmonic oscillator were analyzed in detail.

Study on Lyapunov exponent and Floquet exponent of Duffing oscillator;

Parameter estimation of multifrequency signal by using Duffing oscillator;

Study on detection method of PSK signal based on Duffing oscillator;

Utilizing the idea of the open-plus-closed-loop(OPCL) control,a controller which is composed of an external excitation and linear feedback was designed to entrain the chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits.

The steady state responses and stabilities of complex Duffing oscillator are analyzed by using harmonic balance and homotopy continuation methods.

This thesis discusses the bifurcations and fractals of Holmes-Duffing oscillator under some kinds of excitations.