in this work, time domain analysis is used to solve adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked lc and ring oscillators considering their time-varying nature. then, the analysis is verified...

There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony...

By taking a Klein-Gordon field as the environment of an harmonic oscillator and using a new method for dealing with quantum dissipative systems (minimal coupling method), the quantum dynamics and radiation reaction for a quantum damped harmonic oscillator investigated. Applying perturbation method, some transition probabilities indicating the way energy flows between oscillator, reservoir and q...

We consider the problem of equilibration of a single oscillator system with dynamics given by the generalized classical Langevin equation. It is well-known that this dynamics can be obtained if one considers a model where the single oscillator is coupled to an infinite bath of harmonic oscillators which are initially in equilibrium. Using this equivalence we first determine the conditions neces...

Uncertainty quantification is the state-of-the-art framework dealing with uncertainties arising in all kind of real-life problems. One of the framework’s functions is to propagate uncertainties from the stochastic input factors to the output quantities of interest, hence the name uncertainty propagation. To this end, polynomial chaos expansions (PCE) have been effectively used in a wide variety...

It is shown analytically that pulse solitary waves in a chain with Lermard-Jones type nearest neighbor interaction are strongly localized and marginally stable in the high energy limit. In a damped and periodically driven chain we obtain numerically families of states whose behavior is similar to that of equally many oscillators. We observe a period doubling sequence in a one-solitary wave fami...