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 ...

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...

We study the influence of decaying perturbations on autonomous oscillatory systems in a plane under assumption that preserve equilibrium state limit system, oscillate with asymptotically constant frequency, and satisfy nonresonance condition. discuss long-term behavior perturbed trajectories neighborhood state. describe conditions perturbation parameters guarantee preservation or loss stability...

The nonlinear hysteresis behavior in ferroelectric materials, such as lithium tantalate and lithium niobate, may be explained by dynamical systems analysis. In a previous work, the polarization “domain wall width” was studied in terms of only spatial variation and eventually critical values of polarization were determined to derive the stability zone in the context of Landau-Ginzburg free energ...

The bidimensional Duffing oscillator (2DHD) is a parametric Hamiltonian system, integrable by elliptic functions, which includes as particular cases the isotropic oscillator and the classic Hamiltonian Duffing model. The Stark effect, after the KS transformation is used and the parameters are properly chosen, may be studied as a couple of 2DHD. A particular case of 2DHD system has been consider...

A method for the development of mathematical models for dynamic systems with arbitrary nonlinearides from measured data is described. The method involves the use of neural networks as embedded processors indynamic system simuation models. The technique is demonstrated through generation of models for anharmonic oscillators described by the Duffing Equation and the Van der Pol Equation from meas...

Time-delay is ubiquitous in many dynamical systems. The role of single and multiple time-delay on vibrational resonance in a single Duffing oscillator and in a system of n Duffing oscillators coupled unidirectionally and driven by both a lowand a high-frequency periodic force is presented. The investigation is performed through both theoretical approach and numerical simulation. Theoretically d...

In this paper, periodic motions in a periodically excited, Duffing oscillator with a time-delayed displacement are investigated through the Fourier series, and the stability and bifurcation of such periodic motions are discussed through eigenvalue analysis. The time-delayed displacement is from the feedback control of displacement. The analytical bifurcation trees of period-1 motions to chaos i...