To apply effective methods to analyze and distinguish all kinds of response patterns is an important issue of nonlinear dynamics. This paper contributes to develop an alternative Poincaré section method to analyze and identify the whirl responses of a nonlinear oscillator. This integration for analyzing high-order harmonic and chaotic motions is used to integrate the distance between state traj...

The cutting sound in the audible range includes plenty of tool wear information. The sound is sampled by the acoustic emission AE sensor as a short-time sequence, then worn wear can be detected by the Duffing-Holmes oscillator. A novel engineering method is proposed for determining the chaotic threshold of the Duffing-Holmes oscillator. First, a rough threshold value is calculated by local Lyap...

We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories LPTs . The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an...

Periodically driven oscillators are commonly described in a frame corotating with the drive and using rotating-wave approximation (RWA). This description, however, is known to induce errors for off-resonant driving. Here, we show that standard quantum creation annihilation of particles oscillators' natural frequency, necessarily leads incorrect results when combined RWA. We demonstrate this on ...

This paper proposes a hybrid control scheme for the synchronization of two chaotic Duffing oscillator system, subject to uncertainties and external disturbances. The novelty of this scheme is that the Linear Quadratic Regulation (LQR) control, Sliding Mode (SM) control and Gaussian Radial basis Function Neural Network (GRBFNN) control are combined to chaos synchronization with respect to extern...

A new algorithm is proposed to combine the split-frequency harmonic balance method (SFHBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number ...

We propose a mean-field approach to the Duffing oscillator to construct perturbatively the bounded operators that generate the quantum states, and to define a non-Gaussian density operator. 1 The Duffing oscillator is a typical anharmonic oscillator whose classical aspect is relatively well-understood [1]. It has been studied in many fields of physics from classical mechanics to quantum mechani...

Sustained resonance in a linear oscillator is achievable with a drive whose constant frequency matches the resonant frequency of the oscillator. But in oscillators with nonlinear restoring forces such as the pendulum, Duffing and Duffing-Van der Pol oscillator, the resonant frequency changes as the amplitude changes, so a constant frequency drive results in a beat oscillation instead of sustain...

In this article, under certain parametric conditions, we study the first integrals of the Duffing-van der Pol-type oscillator equations which include the van der Pol and the Duffing oscillator systems, as particular cases. After making a series of variable transformations and applying the PrellerSinger method, we find the first integrals of the simplified equations without complicated calculati...