We analyze the collective dynamics of an ensemble globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where splits into two internally synchronized clusters, as a consequence bistability individual oscillators. The multiplicity these solutions, induced by many possible ways distributing between implies that can exhibit multist...

A modified master-slave scheme to look for synchronization, based on a general combination of elastic and dissipative couplings, is presented. We focus solutions according the presented, illustrating method we use, by employing van der Pol Duffing oscillators analyzing three different ways coupling. find synchronization in oscillators.

We consider the effect of external noise on the dynamics of limit cycle oscillators. The Lyapunov exponent becomes negative under influence of small white noise, what means synchronization of two or more identical systems subject to common noise. We analytically study the effect of small non-identities in the oscillators and in the noise, and derive statistical characteristics of deviations fro...

A rational elliptic balance method is introduced to obtain exact and approximate solutions of nonlinear oscillators by using Jacobi elliptic functions. To illustrate the applicability of the proposed rational elliptic forms in the solution of nonlinear oscillators, we first investigate the exact solution of the non-homogenous, undamped Duffing equation. Then, we introduce first and second order...

The phenomenon of on-off intermittency is studied in two coupled double-well Duffing oscillators with stochastic driving. We demonstrate that by using slow harmonic modulation applied to an accessible system parameter, the intermittent chaotic attractors can be completely eliminated. The influence of noise is also investigated. Power-law scaling of the average laminar time with a critical expon...

In this paper, we present a numerical scheme using uniform Haar wavelet approximation and quasilinearization process for solving some nonlinear oscillator equations. In our proposed work, quasilinearization technique is first applied through Haar wavelets to convert a nonlinear differential equation into a set of linear algebraic equations. Finally, to demonstrate the validity of the proposed m...

We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Mor...

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...

The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force f and its frequency Ω. We first examine the stability of the steady state in linear response, and classify the different types of bifurcation likely to occur in this model. We then explore the complex behaviour associated with these bifurcat...

Self-limiting 46.4-MHz series resonant reference oscillators employing a wine-glass mode disk micromechanical resonator to avoid hard limiting without the need for ALC have achieved measured phase noises of -113 and -134 dBc/Hz at 1kHz and far-fromcarrier offsets, respectively. When divided down to 10MHz frequency for fair comparison with other oscillators, these values correspond to -126 dBc/H...