This paper deals with the dynamics of a model describing systems eonsisting of the classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. Both the forced and autonomous cases are considered. Harmonic response is investigated along with its stability boundaries. Condition for quenching phenomena in the autonomous case is derived. Neimark bifurcation is observed and it is...

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

The standard harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in which the conservative force is additionally expanded as a Fourier sine series in space. As a result, the steady-state oscillation frequency can be expressed in terms of a Bessel series, and the sums of many such series are know...

0960-0779/$ see front matter 2011 Elsevier Ltd doi:10.1016/j.chaos.2011.08.002 ⇑ Corresponding author. Tel.: +55 (11) 3091 6842 6706. E-mail address: [email protected] (E.S. Medeiros). In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak h...

This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of it...

A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this techn...

The paper proposed a new method for the detection of QPSK carrier signal that based on double duffing oscillator to solve the problems as high attenuation and strong noise interference in the QPSK carrier communication of low voltage power line. This method has making use of the different phase of QPSK carrier signal to stimulate the double duffing oscillators to enter different states and thro...

The forced Duffing oscillator is investigated by intentional time-delayed displacement feedback by fast Fourier transform based incremental harmonic balance method along with continuation technique (FFT-IHBC). FFT-IHBC can efficiently develop frequency response curves with all stable and unstable solutions and solution branches. Appreciable reduction in peak value of response and gradual reduct...

We have studied experimentally a chaotic cryptosystem, which is based on the inverse system approach. We applied this method to a second order nonlinear circuit (master circuit), which is described by a Duffing equation. We present the implementation of the slave circuit with the inverse system approach and we demonstrate the decryption when the information signal has several forms (sinusoidal ...

Aiming at the feature extraction of weak periodic signal in early fault of machinery, a novel weak periodic signal detection with Duffing oscillator based on empirical mode decomposition (EMD) was presented. The chaotic character of Duffing oscillator was analyzed, and the Melnikov method of determining chaotic threshold of Duffing oscillators was discussed. The principle of weak signal detecti...