In contrast to the well-known phenomenon of frequency stabilization in a synchronized noisy nonlinear oscillator, little is known about its amplitude stability. this paper, we investigate experimentally and theoretically evolution stability nanomechanical self-sustained oscillator that with an external harmonic drive. We show phase difference between tones plays critical role on level, demonstr...

In the present paper the behavior of an elastically mounted cylinder in low and high mass-damping ratio is investigated. For high mass-damping ratio, a classical wake oscillator model is used. At the first, by neglecting all damping and nonlinear terms of this model, the possibility of using a linear model for determination of the lock-in range and the dominant mode is investigated. Then, w...

Mathematical models of nonlinear oscillators are used to describe a wide variety of physical and biological phenomena that exhibit self-sustained oscillatory behavior. When these oscillators are strongly driven by forces that are periodic in time, they often exhibit a remarkable ‘‘mode-locking’’ that synchronizes the nonlinear oscillations to the driving force. The purpose of this paper is to d...

We derive a coupled-wave theory for backward phase-matched optical parametric amplifiers and oscillators in a dielectric modulated nonlinear optical material. Unlike a forward phase-matched distributed-feedback optical parametric oscillator, a backward oscillator of this type can have high-threshold gap modes at Bragg resonance and low-threshold detuned modes. In addition to the structure feedb...

The dependence of ENSO’s period on its amplitude is examined using a simple delayed oscillator model. This dependence is first calculated in the strongly nonlinear regime by extracting and analyzing unstable periodic orbits from the chaotic attractor of the model. In this regime, the period is found to decrease with increasing amplitude. Next, the dependence of the period on the amplitude is al...

| A numerical noise analysis method for oscillators is proposed. Noise sources are usually small and can be considered as perturbations to a large amplitude oscillation. Transfer functions from each noise source to the oscillator output can be calculated by modeling the oscillator as a linear periodic time-varying circuit. The proposed method is a time domain method and can be applied to strong...

In a single-degree-of-freedom weakly nonlinear oscillator subjected to periodic external excitation, a small-amplitude excitation may produce a relatively large-amplitude response under primary resonance conditions. Jump and hysteresis phenomena that result from saddle-node bifurcations may occur in the steady-state response of the forced nonlinear oscillator. A simple mass-spring-damper vibrat...

By introducing Colpitts oscillator as a chaotic system, this paper deals with back-stepping control method and investigates the restrictions and problems of the controller where non-existence of a suitable response in the presence of uncertainty is the most important problem to note. In this paper, the back-stepping sliding mode method is introduced as a robust method for controlling nonlinear ...

The harmonic oscillator is a paradigm of predictability. The resonance response of a harmonic oscillator can be exploited to make clocks accurate to 1 part in 10. Harmonic oscillations are normally observed in systems operating near equilibrium and governed by linear or “Hooke’s law” restoring forces. Nonetheless, for small enough excursions from equilibrium, systems governed by nonlinear resto...

Nonlinear properties of high-temperature superconducting (HTS) strongly coupled resonators at different input power have been investigated by measurements of the quality factor as a function of input power as well as by generation of the intermodulation distortion (IMD). The double-sided YBCO films on CeO2 buffered sapphire demonstrate advanced performance with the microwave surface resistance ...