A peculiar type of synchronization has been found when two Van der Pol-Duffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and grad...

We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We find close quantitative agreement between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. ...

The current paper focuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of the equation of motion; the variational iteration method, He’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. The results reveal that approxim...

The chaotic synchronization regime in coupled dynamical systems is considered. It has been shown that the onset of a synchronous regime is based on the appearance of a phase relation between the interacting chaotic oscillator frequency components of Fourier spectra. The criterion of synchronization of spectral components as well as the measure of synchronization has been discussed. The universa...

In this study, both the ansatz and averaging methods are carried out for analyzing complex Duffing oscillators including undamped/conserved oscillator (CDO) damped/unconserved CDO to obtain some approximate analytical solutions. To analyze conserved CDO, it is reduced two decoupled oscillators. After that, exact solution of employed derive an approximation in terms Jacobi elliptic function. dam...

We prove that there is an invariant torus with the given Diophantine frequency vector for a class of Hamiltonian systems defined by integrable large function non-autonomous perturbation. As application, we finite network Duffing oscillators periodic external forces possesses Lagrange stability almost all initial data.

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 ...