Chaotic motions of a Rayleigh-Duffing oscillator with periodically external and parametric excitations are investigated rigorously. Chaos arising from intersections of homoclinic orbits is analyzed with the Melnikov method. The critical curves separating the chaotic and non-chaotic regions are obtained. The chaotic feature on the system parameters is discussed. Chaotic dynamics are also compare...

To obtain new ways of detecting weak signals, we analyzed the motion of a Duffing oscillator in different input states by solving the Duffing equation and then elaborating on the basic principles of weak signal detection based on Duffing oscillator phase-change characteristics. The experiment that shows how to achieve weak signal detection with a Duffing oscillator based on virtual instrument t...

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms ...

Due to great noise interference and strong signal attenuation in low voltage power line, two Duffing oscillator methods is proposed to detect QPSK carrier signal. At the same time, after analyzing the law of system solution of Duffing Oscillator, the algorithm of difference distribution of system solution is proposed to identify phase transition, which can greatly decrease calculation. The expe...

In this article, we consider the nonlinear Duffing-van der Pol-type oscillator system by means of the first integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly, we apply the Division Theorem for two variables in the comple...

We present an innovative adaptive, model following control scheme and apply it to control a chaotic system with unknown parameters. We illustrate the proposed approach with control of Duffing oscillator problem. The same idea is used to solve three important problems: suppression of chaos, anticontrol of chaos and chaos synchronization. We propose to use ‘approximators’ linearly parameterized b...

By taking two-coupled duffing oscillator system as the research object, the study found under the synergistic effect of weak periodic signal and noise, the two-coupled duffing oscillator system has typical stochastic resonance and even could achieve better output of stochastic resonance than single duffing oscillator. Based on this phenomenon, this paper proposes a new method to detect the weak...

single-valence electron atoms are an important class of atoms. their oscillator strengths are their important properties. knowing the oscillator strengths one can easity calculate the transition probabilities of the spectral lines and hence the lifetimes of energy levels of most atoms. the oscillator strengths of the spectral lines of most atoms are not knoen with sufficient accuracy due to the...

Weak signal detection is very important in the downhole acoustic telemetry system. This paper introduces the Duffing oscillator weak signal detection method for the downhole acoustic telemetry systems. First, by solving the Duffing equation, analyzed the dynamics characteristic of Duffing oscillator and weak signal detection principle; and then on this basis, built Duffing oscillator circuit ba...