Energy balance method EBM is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the firstand second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreemen...

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...

In this study, a novel analytical solution to the integrable undamping Duffing equation with constant forced term is obtained. Also, new approximate (semianalytical) for nonintegrable linear damping oscillator reported. The given in terms of Weierstrass elliptic function arbitrary initial conditions. With respect it, semianalytical constructed depending on ansatz and exact standard (in absence ...

We find an upper bound for the number of limit cycles, bifurcating from eight-loop Duffing oscillator $$x''= x-x^{3}$$ under special cubic perturbation $$\begin{aligned} x''= x-x^{3}+\lambda _{1}y+\lambda _{2}x^{2}+\lambda _{3}xy+\lambda _{4}x^{2}y. \end{aligned}$$

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...

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...